30 results on '"variation methods"'
Search Results
2. Some results for a supercritical Schrödinger-Poisson type system with (p,q)-Laplacian
- Author
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Hui Liang, Yueqiang Song, and Baoling Yang
- Subjects
schrödinger-poisson type system ,truncation technique ,mountain pass theorem ,variation methods ,moser iterative method ,Mathematics ,QA1-939 - Abstract
In this work, we focus our attention on the existence of nontrivial solutions to the following supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian: $ \begin{equation*} \begin{cases} -\Delta_{p}u-\Delta_{q}u+\phi|u|^{q-2} u = f\left(x, u\right)+\mu|u|^{s-2} u & \text { in } \Omega, \\ -\Delta \phi = |u|^q & \text { in } \Omega, \\ u = \phi = 0 & \text { on } \partial \Omega, \end{cases} \end{equation*} $ where $ \Omega \subset \mathbb{R}^N $ is a bounded smooth domain, $ \mu > 0, N > 1 $, and $ -\Delta_{{\wp}}\varphi = div(|\nabla\varphi|^{{\wp}-2} \nabla\varphi) $, with $ {\wp}\in \{p, q\} $, is the homogeneous $ {\wp} $-Laplacian. $ 1 < p < q < \frac{q^*}{2} $, $ q^*: = \frac{Nq}{N-q} < s $, and $ q^* $ is the critical exponent to $ q $. The proof is accomplished by the Moser iterative method, the mountain pass theorem, and the truncation technique. Furthermore, the $ (p, q) $-Laplacian and the supercritical term appear simultaneously, which is the main innovation and difficulty of this paper.
- Published
- 2024
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3. Study on Variation in the Subtitle Translation of Films with Revolutionary Themes in Terms of Audiences’ Reception
- Author
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Lu, Xiuying, Xu, Xiaoxue, Striełkowski, Wadim, Editor-in-Chief, Black, Jessica M., Series Editor, Butterfield, Stephen A., Series Editor, Chang, Chi-Cheng, Series Editor, Cheng, Jiuqing, Series Editor, Dumanig, Francisco Perlas, Series Editor, Al-Mabuk, Radhi, Series Editor, Scheper-Hughes, Nancy, Series Editor, Urban, Mathias, Series Editor, Webb, Stephen, Series Editor, Sedon, Mohd Fauzi bin, editor, Khan, Intakhab Alam, editor, BİRKÖK, Mehmet CÜNEYT, editor, and Chan, KinSun, editor
- Published
- 2023
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4. Nontrivial Solutions for a (p, q)-Type Critical Choquard Equation on the Heisenberg Group.
- Author
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Yang, Baoling, Zhang, Deli, and Liang, Sihua
- Abstract
In this paper, we consider a critical (p, q) equation on the Heisenberg group of the following form: - Δ H , p u - Δ H , q u + V (ξ) (| u | p - 2 u + | u | q - 2 u) = μ ∫ H n F (ξ , u) | η - 1 ξ | λ d ξ f (η , u) + | u | q ∗ - 2 u ,
where the operator - Δ H , ℘ φ = div H (| D H φ | H ℘ - 2 D H φ) , with ℘ ∈ { p , q } , is the proverbial horizontal ℘ -Laplacian on the Heisenberg group, 1 < p < (2 Q - λ) 2 Q q < q < Q , q ∗ = q Q / (Q - q) is the critical exponent, and Q = 2 n + 2 is the homogeneous dimension of H n , μ and λ are some real parameters. Under the appropriate assumptions of potential functions V and f, the existence of entire solutions to the above equation on the Heisenberg group is obtained by using the mountain pass theorem and the concentration compactness principle. The results presented here extend or complete recent papers and are new to critical equations involving (p, q)-Laplacian operators and convolution terms on Heisenberg group. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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5. Critical equations with Hardy terms in the Heisenberg group.
- Author
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Pucci, Patrizia and Temperini, Letizia
- Abstract
In this paper, we are concerned with the study of a critical (p, q) equation with Hardy terms on the Heisenberg group. Existence of entire solutions is obtained via an application of some concentration–compactness type results and the mountain pass theorem. Our results are presented in the model case of the (p, q) horizontal Laplacian equations, but the method can be extended to deal with a more general class of problems with operators of (p, q) growth. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. Least energy sign-changing solutions of Kirchhoff equation on bounded domains
- Author
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Xia Li, Wen Guan, and Da-Bin Wang
- Subjects
kirchhoff equation ,nonlocal term ,variation methods ,sign-changing solutions ,Mathematics ,QA1-939 - Abstract
We deal with sign-changing solutions for the Kirchhoff equation $ \begin{cases} -(a+ b\int _{\Omega}|\nabla u|^{2}dx)\Delta u = \lambda u+\mu|u|^{2}u, \; \ x\in\Omega, \\ u = 0, \; \ x\in \partial\Omega, \end{cases} $ where $ a, b > 0 $ and $ \lambda, \mu\in\mathbb{R} $ being parameters, $ \Omega\subset \mathbb{R}^{3} $ is a bounded domain with smooth boundary $ \partial\Omega $. Combining Nehari manifold method with the quantitative deformation lemma, we prove that there exists $ \mu^{\ast} > 0 $ such that above problem has at least a least energy sign-changing (or nodal) solution if $ \lambda < a\lambda_{1} $ and $ \mu > \mu^{\ast} $, where $ \lambda_{1} > 0 $ is the first eigenvalue of $ (-\Delta u, H^{1}_{0}(\Omega)) $. It is noticed that the nonlinearity $ \lambda u+\mu|u|^{2}u $ fails to satisfy super-linear near zero and super-three-linear near infinity, respectively.
- Published
- 2022
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7. Sign-changing solutions for a class of fractional Kirchhoff-type problem with logarithmic nonlinearity
- Author
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Qing Yang and Chuanzhi Bai
- Subjects
fractional kirchhoff-schrodinger-type equation ,sign-changing solutions ,logarithmic nonlinearity ,variation methods ,Mathematics ,QA1-939 - Abstract
In this paper, we are interested the following fractional Kirchhoff-type problem with logarithmic nonlinearity \begin{equation*} \left\{ \begin{array} {ll} \left(a+b \iint_{\Omega^2} \frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}} dxdy\right)(-\Delta)^s u + V(x)u = Q(x) |u|^{p-2}u \ln u^2, & {\rm in } \ \Omega, \\ u=0, & {\rm in } \ \mathbb{R}^N \setminus \Omega, \end{array} \right. \end{equation*} where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain, $N > 2s$ ($0 < s < 1$), $(-\Delta)^s$ is the fractional Laplacian, $V, Q$ are continuous, $V, Q \ge 0$. $a, b > 0$ are constants, $4 < p < 2_s^* := \frac{2N}{N-2s}$. By using constraint variational method, a quantitative deformation lemma and some analysis techniques, we obtain the existence of ground state sign-changing solutions for above problem.
- Published
- 2021
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8. Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth
- Author
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Jun Lei and Hongmin Suo
- Subjects
kirchhoff type equation ,neumann problem ,critical growth ,variation methods ,nontrivial solution ,Mathematics ,QA1-939 - Abstract
In this paper, we consider a Neumann problem of Kirchhoff type equation \begin{equation*} \begin{cases} \displaystyle-\left(a+b\int_{\Omega}|\nabla u|^2dx\right)\Delta u+u= Q(x)|u|^4u+\lambda P(x)|u|^{q-2}u, &\rm \mathrm{in}\ \ \Omega, \\ \displaystyle\frac{\partial u}{\partial v}=0, &\rm \mathrm{on}\ \ \partial\Omega, \end{cases} \end{equation*} where $\Omega$ $\subset$ $\mathbb{R}^3$ is a bounded domain with a smooth boundary, $a,b>0$, $10$ is a real parameter, $Q(x)$ and $P(x)$ satisfy some suitable assumptions. By using the variational method and the concentration compactness principle, we obtain the existence and multiplicity of nontrivial solutions.
- Published
- 2021
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9. Existence of least energy nodal solution for Kirchhoff-type system with Hartree-type nonlinearity
- Author
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Jin-Long Zhang and Da-Bin Wang
- Subjects
nonlocal term ,variation methods ,nodal solutions ,Mathematics ,QA1-939 - Abstract
This paper deals with following Kirchhoff-type system with critical growth \[\begin{cases} -(a+ b\int _{\mathbb{R}^3}|\nabla u|^{2}dx)\Delta u+ V(x)u+\phi|u|^{p-2}u =|u|^{4}u+\mu f(u), ~\ x\in\mathbb{R}^3,\\ (-\Delta)^{\alpha/2}\phi=l|u|^p, ~\ x\in \mathbb{R}^3, \end{cases}\] where $a, \mu>0$, $b, l\geq0$, $\alpha\in(0,3)$, $p\in[2,3)$ and $\phi|u|^{p-2}u$ is a Hartree-type nonlinearity. By the minimization argument on the nodal Nehari manifold and the quantitative deformation lemma, we prove that the above system has a least energy nodal solution. Our result improve and generalize some interesting results which were obtained in subcritical case.
- Published
- 2020
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10. Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity
- Author
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Ya-Lei Li, Da-Bin Wang, and Jin-Long Zhang
- Subjects
p-laplacian kirchhoff-type equation ,nonlocal term ,variation methods ,sign-changing solutions ,Mathematics ,QA1-939 - Abstract
"In this paper, we study the existence of ground state sign-changing solutions for following $p$-Laplacian Kirchhoff-type problem with logarithmic nonlinearity\begin{equation*} \left\{ \renewcommand{\arraystretch}{1.25} \begin{array}{ll} -(a+ b\int _{\Omega}|\nabla u|^{p}dx)\Delta_p u=|u|^{q-2}u\ln u^2, ~x\in\Omega \\ u=0, ~\ x\in \partial\Omega, \end{array} \right.\end{equation*}where $\Omega\subset \mathbb{R}^{N}$ is a smooth bounded domain, $a, b>0$ are constant, 4 ≤ 2p < q < p* and N > p. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains."
- Published
- 2020
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11. Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$
- Author
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Da-Bin Wang, Tian-Jun Li, and Xinan Hao
- Subjects
Sign-changing solution ,Nonlocal term ,Variation methods ,Analysis ,QA299.6-433 - Abstract
Abstract In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: {−(a+b∫R3|∇u|2dx)Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2}, &x\in \mathbb{R}^{3}, \end{cases} $$ where a, b are positive constants, V∈C(R3,R+) $V\in \mathcal{C}(\mathbb{R} ^{3},\mathbb{R}^{+})$. By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution ub $u_{b}$ to this problem, and study the energy property of ub $u_{b}$. Moreover, we investigate the asymptotic behavior of ub $u_{b}$ as the parameter b↘0 ${b\searrow 0}$.
- Published
- 2019
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12. Least energy sign-changing solutions for fourth-order Kirchhoff-type equation with potential vanishing at infinity.
- Author
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Zhang, Hua-Bo and Guan, Wen
- Abstract
In this paper, we study the following fourth-order Kirchhoff-type equation Δ 2 u - a + b ∫ R N | ∇ u | 2 d x Δ u + V (x) u = K (x) f (u) , x in R N , with the potential V(x) vanishing at infinity. Under suitable conditions, by using constraint variational method and the quantitative deformation lemma, we obtain a least energy sign-changing (or nodal) solution to this problem. Moreover, we prove that this least energy sign-changing solution has precisely two nodal domains. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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13. Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth.
- Author
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Wang, Da-Bin, Zhang, Hua-Bo, and Guan, Wen
- Abstract
In this paper, we study the following Schrödinger-Poisson system { − Δ u + V (x) u + λ ϕ u = | u | 4 u + μ f (u) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , where V (x) is a smooth function and μ , λ > 0. Under suitable conditions on f , by using constraint variational method and the quantitative deformation lemma, if μ is large enough, we obtain a least-energy sign-changing (or nodal) solution u λ to this problem for each λ > 0 , and its energy is strictly larger than twice that of the ground state solutions. Moreover, we study the asymptotic behavior of u λ as the parameter λ ↘ 0. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
14. Sign-changing solutions for a class of fractional Kirchhoff-type problem with logarithmic nonlinearity
- Author
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Chuanzhi Bai and Qing Yang
- Subjects
Physics ,fractional kirchhoff-schrodinger-type equation ,Class (set theory) ,Logarithm ,General Mathematics ,variation methods ,lcsh:Mathematics ,sign-changing solutions ,lcsh:QA1-939 ,Omega ,Combinatorics ,Nonlinear system ,Variational method ,Bounded function ,Domain (ring theory) ,Ground state ,logarithmic nonlinearity - Abstract
In this paper, we are interested the following fractional Kirchhoff-type problem with logarithmic nonlinearity \begin{equation*} \left\{ \begin{array} {ll} \left(a+b \iint_{\Omega^2} \frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}} dxdy\right)(-\Delta)^s u + V(x)u = Q(x) |u|^{p-2}u \ln u^2, & {\rm in } \ \Omega, \\ u=0, & {\rm in } \ \mathbb{R}^N \setminus \Omega, \end{array} \right. \end{equation*} where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain, $N > 2s$ ($0 < s < 1$), $(-\Delta)^s$ is the fractional Laplacian, $V, Q$ are continuous, $V, Q \ge 0$. $a, b > 0$ are constants, $4 < p < 2_s^* := \frac{2N}{N-2s}$. By using constraint variational method, a quantitative deformation lemma and some analysis techniques, we obtain the existence of ground state sign-changing solutions for above problem.
- Published
- 2021
15. Multiple solutions to elliptic equations on $\mathbb{R}^N$ with combined nonlinearities
- Author
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Anran Li and Chongqing Wei
- Subjects
weighted sobolev embedding ,sublinear ,asymptotically linear ,superlinear ,critical point theory ,variation methods ,Mathematics ,QA1-939 - Abstract
In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equation \begin{equation*} \begin{cases} - \Delta u +V(x)u = -\lambda Q(x)|u|^{q-2}u+ Q(x)f(u),\quad x\in\mathbb{R}^N,\\ u(x)\rightarrow 0,\quad \hbox{as}\ |x|\rightarrow +\infty,\end{cases} \tag*{(P)$_\lambda$} \end{equation*} where $1
- Published
- 2015
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16. On critical double phase Choquard problems with singular nonlinearity.
- Author
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Yang, Baoling, Zhang, Deli, and Liang, Sihua
- Abstract
In this article, we consider the following double phase problem with singular term and convolution term − Δ p u − Δ q u = λ u − γ + ∫ Ω | u | q μ ∗ | x − y | μ d y | u | q μ ∗ − 2 u in Ω , u > 0 in Ω , u = 0 on ∂ Ω , where Ω is a bounded domain in R N with Lipschitz boundary ∂ Ω , γ ∈ (0 , 1) , 1 < p < q < q μ ∗ , − Δ ℘ φ = d i v ( | ∇ φ | ℘ − 2 ∇ φ) , with ℘ ∈ { p , q } , is the homogeneous ℘ -Laplacian. λ > 0 is a real parameter, 0 < μ < N , N > p and q μ ∗ = (p N − p μ / 2) / (N − p) is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. The existence of at least one weak solution is obtained for the above problem by using the Nehari manifold approach. • The background of critical double phase Choquard problems is rather outstanding. Moreover, the study of critical problems is deeply connected to the concentration phenomena taking place when considering sequences of approximated solutions. • The main innovation and difficulty of this problem is that the critical term and singular nonlinearity appear simultaneously. In order to overcome these difficulties, we establish a truncation parameter, and combine with a subtle gradient analysis, to verify the solution sequence converges to this problem virtually. • This paper extends some existence results of problem concerning the existence of solutions to this problem in the subcritical case. Moreover, the emergence of p and q -Laplacian operator makes the study of this problem more complicated and interesting. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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17. Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth
- Author
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Hongmin Suo and Jun Lei
- Subjects
Physics ,kirchhoff type equation ,variation methods ,lcsh:Mathematics ,General Mathematics ,neumann problem ,Boundary (topology) ,Multiplicity (mathematics) ,lcsh:QA1-939 ,Omega ,critical growth ,nontrivial solution ,Combinatorics ,Compact space ,Bounded function ,Domain (ring theory) ,Neumann boundary condition ,Nabla symbol - Abstract
In this paper, we consider a Neumann problem of Kirchhoff type equation \begin{equation*} \begin{cases} \displaystyle-\left(a+b\int_{\Omega}|\nabla u|^2dx\right)\Delta u+u= Q(x)|u|^4u+\lambda P(x)|u|^{q-2}u, &\rm \mathrm{in}\ \ \Omega, \\ \displaystyle\frac{\partial u}{\partial v}=0, &\rm \mathrm{on}\ \ \partial\Omega, \end{cases} \end{equation*} where $\Omega$ $\subset$ $\mathbb{R}^3$ is a bounded domain with a smooth boundary, $a,b>0$, $10$ is a real parameter, $Q(x)$ and $P(x)$ satisfy some suitable assumptions. By using the variational method and the concentration compactness principle, we obtain the existence and multiplicity of nontrivial solutions.
- Published
- 2021
18. Critical equations with Hardy terms in the Heisenberg group
- Author
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Patrizia Pucci and Letizia Temperini
- Subjects
Variation methods ,General Mathematics ,Hardy terms ,critical exponents ,Heisenberg group, Variation methods, critical exponents, Hardy terms ,Heisenberg group - Abstract
In this paper, we are concerned with the study of a critical (p, q) equation with Hardy terms on the Heisenberg group. Existence of entire solutions is obtained via an application of some concentration–compactness type results and the mountain pass theorem. Our results are presented in the model case of the (p, q) horizontal Laplacian equations, but the method can be extended to deal with a more general class of problems with operators of (p, q) growth.
- Published
- 2022
19. Non-linear Models' Researching.
- Author
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Sheyretski, Kostadin and Lazarova, Meglena
- Subjects
NONLINEAR equations ,DIFFERENTIAL equations - Abstract
In this paper we consider a common used in economic pendulum's nonlinear equation. A Galiorkin's variation method is introduced. For solving the concrete differential equation we use a combination of the variation method and the method of the step by step consideration. The solutions that we obtain are useful for analyses and researching of the systems' quality behavior. On the other hand these systems are constructed of equations which are equivalent to the equations used in the economic systems. [ABSTRACT FROM AUTHOR]
- Published
- 2015
20. ВАРИАЦИОННЫЙ ПРИНЦИП И ЭНЕРГЕТИКА ДЕФОРМАЦИЙ ПРИКЛАДНОЙ МОДЕЛИ МИКРОПОЛЯРНОГО УПРУГОГО КРУГОВОГО ТОНКОГО СТЕРЖНЯ.
- Author
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Саркисян, С. О. and Хачатрян, М. В.
- Abstract
In the present paper the general variation principle of plane stress state of micropolar theory of elasticity is considered in a circular area, on the basis of which the basic equations and boundary conditions of the mentioned theory are obtained. Accepting the known hypotheses of the construction of the theory of micropolar elastic thin straight bars, plates and shells, general variation principle for applied model of micropolar elastic circular thin bars with transverse shear deformations is obtained on the basis of variation principle of plane stress state. Based on the constructed variation principle the basic equations and natural boundary conditions of applied model of micropolar elastic circular thin bar are obtained. It is confirmed that all energy theorems and Ritz, Bubnov-Galerkin, FEM variation methods are applicable for the constructed model of micropolar elastic circular thin bar and for solutions of corresponding boundary value problems of the applied model. [ABSTRACT FROM AUTHOR]
- Published
- 2016
21. Multiple solutions to elliptic equations on RN with combined nonlinearities.
- Author
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Anran Li and Chongqing Wei
- Subjects
- *
NUMERICAL solutions to elliptic equations , *NONLINEAR theories , *CRITICAL point theory , *SOBOLEV spaces , *INFINITY (Mathematics) - Abstract
In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equation ... where ... and Q are radial positive functions, which can be vanishing or coercive at infinity, f is asymptotically linear or superlinear at infinity. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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22. A Semi-Classical, Microscopic Model for Nuclear Collective Rotation Plus RPA.
- Author
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Gulshani, P.
- Subjects
- *
NUCLEAR physics , *PHYSICS , *SCHRODINGER equation , *PARTIAL differential equations , *PARTICLES (Nuclear physics) - Abstract
Collective rotation and vibration of deformed nuclei are described semiclassically but microscopically by first transforming the time-dependent Schrodinger equation to a rotating frame, while preserving time-reversal invariance, and then applying a variational method. The rotating-frame axes are chosen to coincide with the principal axes of the expectation of an arbitrary, symmetric second-rank tensor operator Γ⁁. It is shown that the equations derived for the rotational and vibrational motions decouple completely due to the rotational invariance of the Hamiltonian and diagonality of the expectation of Γ⁁ in the rotating frame. The equations describing the vibration reduce to those of the RPA. The equation describing the rotation generalizes that of the conventional cranking model (CM). The predicted rotation moment of inertia is shown to reduce to that of the CM for special types of particle interactions. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
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23. Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3
- Author
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Wang, Da-Bin, Li, Tian-Jun, and Hao, Xinan
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- 2019
- Full Text
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24. STANDING WAVES OF THE DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS WITH GROWING POTENTIALS.
- Author
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Guoping Zhang and Pankov, Alexander
- Subjects
- *
STANDING waves , *SCHRODINGER equation , *NONLINEAR evolution equations , *EMBEDDING theorems , *EMBEDDINGS (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper we investigate the existence of nontrivial standing wave solution of the discrete nonlinear Schrödinger equation with the growing potential at infinity. Firstly we derive a discrete version of compact embedding theorem. Then combining the Nehari manifold approach and the compact embedding theorem we show the existence of nontrivial standing wave solution without Palais-Smale condition. We also prove the exponential decay of the standing wave solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2008
25. Existence and orbital stability of normalized solutions for nonlinear Schrödinger equations
- Author
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Gou, Tianxiang, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Université Bourgogne Franche-Comté, and Louis Jeanjean
- Subjects
Variation methods ,Prescribed L2 norm ,Orbital stability ,Explosion ,Stabilité orbitale ,Réarragement ,Nonlinear Schrödinger equations ,Blowup ,Méthodes variationnelles ,Normalized solutions ,Rearrangemnent ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,Equation de Schrödinger no linaires ,[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] ,Solutions spécialisées ,Norme L2 prescrite - Abstract
In this thesis, we are concerned with the existence and orbital stability of solutions having prescribed -norm for two types of nonlinear Schrödinger equations in , namely a class of coupled nonlinear Schrödinger systems in and a class of fourth-order nonlinear Schrödinger equations in . These two types of nonlinear Schrödinger equations arise in a variety of mathematical and physical models, and have drawn wide attention to research in recent years. From a physical point of view, such solutions are often referred as normalized solutions, which correspond to critical points of the underlying energy functional restricted to -norm constraint. The main ingredients of our proofs are variational methods.; Dans cette thèse nous étudions l’existence et la stabilité orbitale de solutions ayant une norme prescrite pour deux types d’équations Schrödinger non linéaires dans , à savoir, une classe de systèmes non linéaires couplés de Schrödinger dans et une classe d’équations non linéaires de Schrödinger du quatrième ordre dans . Ces deux types d’équations non linéaires de Schrödinger surviennent dans de nombreuses applications en mathématiques et physique, et sont devenus une grande attention dans les années récentes. D’un point de vue physique, de telles solutions sont souvent référées comme des solutions normalisées, qui sont obtenues comme points critiques d’énergie fonctionnelle associée sous contrainte avec une norme. Les éléments clés de nos preuves sont les méthodes variationnelles.
- Published
- 2017
26. Solutions normalisées pour équations de Schrödinger
- Author
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Gou, Tianxiang, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Université Bourgogne Franche-Comté, and Louis Jeanjean
- Subjects
Variation methods ,Prescribed L2 norm ,Orbital stability ,Explosion ,Stabilité orbitale ,Réarragement ,Nonlinear Schrödinger equations ,Blowup ,Méthodes variationnelles ,Normalized solutions ,Rearrangemnent ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,Equation de Schrödinger no linaires ,[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] ,Solutions spécialisées ,Norme L2 prescrite - Abstract
In this thesis, we are concerned with the existence and orbital stability of solutions having prescribed -norm for two types of nonlinear Schrödinger equations in , namely a class of coupled nonlinear Schrödinger systems in and a class of fourth-order nonlinear Schrödinger equations in . These two types of nonlinear Schrödinger equations arise in a variety of mathematical and physical models, and have drawn wide attention to research in recent years. From a physical point of view, such solutions are often referred as normalized solutions, which correspond to critical points of the underlying energy functional restricted to -norm constraint. The main ingredients of our proofs are variational methods.; Dans cette thèse nous étudions l’existence et la stabilité orbitale de solutions ayant une norme prescrite pour deux types d’équations Schrödinger non linéaires dans , à savoir, une classe de systèmes non linéaires couplés de Schrödinger dans et une classe d’équations non linéaires de Schrödinger du quatrième ordre dans . Ces deux types d’équations non linéaires de Schrödinger surviennent dans de nombreuses applications en mathématiques et physique, et sont devenus une grande attention dans les années récentes. D’un point de vue physique, de telles solutions sont souvent référées comme des solutions normalisées, qui sont obtenues comme points critiques d’énergie fonctionnelle associée sous contrainte avec une norme. Les éléments clés de nos preuves sont les méthodes variationnelles.
- Published
- 2017
27. Variāciju metodes elastomēra amortizatora ar saliktu konfigurāciju aprēķināšanai
- Author
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Gonca, V and Švabs, J
- Subjects
functional ,variation methods ,surfaces of crushing ,elastometric absorber ,deposit - Abstract
Elastomēra amortizatoram ir dažādas ģeometriskas formas. Dažiem elastomēra amortizatoriem ir salikta ģeometriska forma. Efektīvai elastomēra amortizatoru ar saliktu ģeometrisku formu izmantošanai ir nepieciešams aprēķināt šī amortizatora stiprības īpašības. Šajā rakstā ir aprakstīta metodika, ar kuras palīdzību var aprēķināt sakarību spēks – nosēde elastomēra amortizatoram ar jebkuru ģeometrisku formu pie statiskas slodzes. Tomēr sarežģītas konstrukcijas detaļām vai tādām, kas sastāv no labi kontaktējošām daļām, kuras izgatavotas no dažādiem materiāliem, veidojot tuvinātos risinājumus, var izrādīties ērti izmantot tādus , kuriem katrā apgabalā ir sava izteiksme. „Veco” funkcionāļu izmantošana šajā gadījumā prasa, lai tiktu ievērots meklējamo funkciju nepārtrauktības nosacījums, pārejot apgabalu sadalījuma robežas. Praksē tas var novest pie liela aprēķinu darba apjoma vai pie neiespējamības izvēlēties meklējamās funkcijas. Pragera aplūkotās tiešās metodes ar funkcionāļiem ļauj samazināt parastās pārvietojumu lauku, spriegumu un deformāciju nepārtrauktības prasības uz pētāmo apgabalu sadalīšanas virsmām uz vairākiem apakšapgabaliem.. Pie tam tiek pieļauta nepārtrauktības nosacījuma neizpildīšanās vai nu pārvietojumiem, vai spēkiem. Izrādās, ka nepārtrauktības prasības var samazināt vēl vairāk
- Published
- 2010
28. Návrh a výpočet membránové konstrukce zastřešení stadionu
- Author
-
Němec, Ivan, Kytýr,, Jií, Němec, Ivan, and Kytýr,, Jií
- Abstract
Tato práce se zabývá problematikou návrhu a výpočtu membránové konstrukce zastřešení stadionu. Jedná se o komplexní inženýrský problém, který v sobě zahrnuje mnoho dílčích složek: hledání počátečního tvaru membrány, staticky i architektonicky vhodné uspořádání systému nosných lan, hospodárné řešení okrajových podmínek (uložení) konstrukce. Všechny složky návrhu se ovlivňují a nelze je řešit bez vzájemné koordinace. Vždy velice záleží na zkušenostech a citu inženýra, jenž takovouto konstrukci navrhuje. Úlohu již není možné řešit dle teorie I.řádu. Rovnováha sil na nedeformované konstrukci, jenž u mnoha projektovaných konstrukcí dává uspokojivé výsledky, by neodpovídala realitě. Je proto nutné uvažovat rovnováhu sil na deformované konstrukci dle teorie velkých deformací. Práce byla zadána s ohledem na záměr firem Ing. Software Dlubal s.r.o. a FEM consulting s.r.o., které spolupracují na vývoji software RFEM, doplnit tento programový systém o modul MEMBRÁNA pro hledání výchozích tvarů membránových konstrukcí. Tato práce má být příspěvkem k vytvoření tohoto modulu., This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.
29. Návrh a výpočet membránové konstrukce zastřešení stadionu
- Author
-
Němec, Ivan, Kytýr,, Jií, Němec, Ivan, and Kytýr,, Jií
- Abstract
Tato práce se zabývá problematikou návrhu a výpočtu membránové konstrukce zastřešení stadionu. Jedná se o komplexní inženýrský problém, který v sobě zahrnuje mnoho dílčích složek: hledání počátečního tvaru membrány, staticky i architektonicky vhodné uspořádání systému nosných lan, hospodárné řešení okrajových podmínek (uložení) konstrukce. Všechny složky návrhu se ovlivňují a nelze je řešit bez vzájemné koordinace. Vždy velice záleží na zkušenostech a citu inženýra, jenž takovouto konstrukci navrhuje. Úlohu již není možné řešit dle teorie I.řádu. Rovnováha sil na nedeformované konstrukci, jenž u mnoha projektovaných konstrukcí dává uspokojivé výsledky, by neodpovídala realitě. Je proto nutné uvažovat rovnováhu sil na deformované konstrukci dle teorie velkých deformací. Práce byla zadána s ohledem na záměr firem Ing. Software Dlubal s.r.o. a FEM consulting s.r.o., které spolupracují na vývoji software RFEM, doplnit tento programový systém o modul MEMBRÁNA pro hledání výchozích tvarů membránových konstrukcí. Tato práce má být příspěvkem k vytvoření tohoto modulu., This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.
30. Návrh a výpočet membránové konstrukce zastřešení stadionu
- Author
-
Němec, Ivan, Kytýr,, Jií, Němec, Ivan, and Kytýr,, Jií
- Abstract
Tato práce se zabývá problematikou návrhu a výpočtu membránové konstrukce zastřešení stadionu. Jedná se o komplexní inženýrský problém, který v sobě zahrnuje mnoho dílčích složek: hledání počátečního tvaru membrány, staticky i architektonicky vhodné uspořádání systému nosných lan, hospodárné řešení okrajových podmínek (uložení) konstrukce. Všechny složky návrhu se ovlivňují a nelze je řešit bez vzájemné koordinace. Vždy velice záleží na zkušenostech a citu inženýra, jenž takovouto konstrukci navrhuje. Úlohu již není možné řešit dle teorie I.řádu. Rovnováha sil na nedeformované konstrukci, jenž u mnoha projektovaných konstrukcí dává uspokojivé výsledky, by neodpovídala realitě. Je proto nutné uvažovat rovnováhu sil na deformované konstrukci dle teorie velkých deformací. Práce byla zadána s ohledem na záměr firem Ing. Software Dlubal s.r.o. a FEM consulting s.r.o., které spolupracují na vývoji software RFEM, doplnit tento programový systém o modul MEMBRÁNA pro hledání výchozích tvarů membránových konstrukcí. Tato práce má být příspěvkem k vytvoření tohoto modulu., This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.
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