Search

The mixed problem for nonlinear strongly dissipative wave equations with acoustic transmission conditions is considered. An existence and uniqueness theorem for local solutions is proved using the Faedo–Galerkin approximations, the compactness method, and the fixed point theorem. The existence of global solutions of this problem is also proved.

In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg–Lévy, Khinchine, Lindeberg–Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances. The final sections review cases of the central limit theorem under non-standard conditions and α-stable convergence.

A topological fuzzy fixed point theorem is given, when generalizing and improving the main result by Diamond, Kloeden and Pokrovskii (1997) [1] . Apart from the sole existence, a weak local stability property, called non-ejectivity in the sense of Browder, of fuzzy fixed points is established. This theorem is then applied for obtaining non-ejective fuzzy fractals. An alternative approach via the Knaster–Tarski theorem is also presented.

In this paper, the existence of solutions for an initial value problem of a fractional differential equation is obtained by means of Monch's fixed point theorem and the technique of measures of noncompactness. AMS (MOS) Subject Classification. 26A33, 34B10, 34G20

In this paper, we study a variant of the state-dependent sweeping process with velocity constraint. The constraint \begin{document}$ {C(\cdot, u)} $\end{document} depends upon the unknown state \begin{document}$ u $\end{document} , which causes one of the main difficulties in the mathematical treatment of quasi-variational inequalities. Our aim is to show how a fixed point approach can lead to an existence theorem for this implicit differential inclusion. By using Schauder's fixed point theorem combined with a recent existence and uniqueness theorem in the case where the moving set \begin{document}$ C $\end{document} does not depend explicitly on the state \begin{document}$ u $\end{document} (i.e. \begin{document}$ C: = C(t) $\end{document} ) given in [ 4 ], we prove a new existence result of solutions of the quasi-variational sweeping process in the infinite dimensional Hilbert spaces with a velocity constraint. Contrary to the classical state-dependent sweeping process, no conditions on the size of the Lipschitz constant of the moving set, with respect to the state, is required.

This paper is devoted to the study of a hypoelliptic Robin boundary value problem for quasilinear, second-order elliptic differential equations depending nonlinearly on the gradient. More precisely, we prove an existence and uniqueness theorem for the quasilinear hypoelliptic Robin problem in the framework of Holder spaces under the quadratic gradient growth condition on the nonlinear term. The proof is based on the comparison principle for quasilinear problems and the Leray–Schauder fixed point theorem. Our result extends earlier theorems due to Nagumo, Ako and Schmitt to the hypoelliptic Robin case which includes as particular cases the Dirichlet, Neumann and regular Robin problems.

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan c1.

The fact that every combinator has a fixed point is at the heart of the λ -calculus as a model of computation. We consider several aspects of such phenomenon; our specific, perhaps eccentric, point of view focuses on problems and results that we consider worthy of further investigations. We first consider the relation with self application, in comparison with the opposite view, which stresses the role of coding, unifying the first and the second fixed point theorems. Then, we consider the relation with the diagonal argument, a relation which is at the origin of the fixed point theorem itself. We also review the Recursion Theorem, which is considered a recursion theoretic version of the fixed point theorem. We end considering systems of equations which are related to fixed points.

In this work, we give sufficient conditions for the existence of a mild solution for some impulsive integro-differential equations in Banach spaces. We study the existence without assuming the Lipschitz condition on the nonlinear term f. The compactness on the C0-semigroup(T(t))t≥0 in a Banach space is not needed. We use Hausdorff’s measure of noncompactness, resolvent operators and Darbo’s fixed point Theorem to obtain the main result of this work. Keywords: Impulsive integro-differential equations, Mild solutions, Sadovskii’s fixed point Theorem, Resolvent operators, Noncompactness measures

In 1995, Palfy and Szabo stated the theorem that a projective space satisfies the six-cross theorem if and only if it is Desarguesian. A mistake in their proof is corrected. Moreover, for projective planes, the three-cross theorem of Palfy and Szabo is identified as the Reidemeister condition.

We study the following fractional Yamabe-type equation: { A s ⁢ u = u n + 2 ⁢ s n - 2 ⁢ s , u > 0 in ⁢ Ω , u = 0 on ⁢ ∂ ⁡ Ω , \left\{\begin{aligned} \displaystyle A_{s}u&\displaystyle=u^{\frac{n+2s}{n-2s}% },\\ \displaystyle u&\displaystyle>0&&\displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right. Here Ω is a regular bounded domain of ℝ n {\mathbb{R}^{n}} , n ≥ 2 {n\geq 2} , and A s {A_{s}} , s ∈ ( 0 , 1 ) {s\in(0,1)} , represents the fractional Laplacian operator ( - Δ ) s {(-\Delta)^{s}} in Ω with zero Dirichlet boundary condition. We investigate the effect of the topology of Ω on the existence of solutions. Our result can be seen as the fractional counterpart of the Bahri–Coron theorem [3].

In this paper, a generalized fixed point theorem and its results are established in the concept of multiplicative distance which was introduced by Agamirza et.al [3] to improve the non-Newtonian calculus. Our results include some existing results in the concept of multiplicative metric space.

We study the existence of positive periodic solutions for a second order differential equation which is related to the Liebau phenomenon. The proof is based on the fixed point theorem in cones. Our results improve and generalize those in the literature.

Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinearities, see (D1) and (D2) in Theorem 3.1, are weaker than known ones, (i.e., (A) in Introduction section). The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

The aim of this work is to present new abstract fixed point theorems in ordered Banach spaces and on Banach algebras. The main existence results generalize Krasnosel’skii’s fixed point theorem of compression and expansion to a class of $$\alpha $$ -homogeneous operators and monotone operators. Two applications to nonlinear Hammerstein integral equations, one of which is of fractional order, are provided together with a numerical example.

We investigate the validity of the Mean Ergodic Theorem in symmetric Banach function spaces E . The assertion of that theorem always holds when E is separable, whereas the situation is more delicate when E is non-separable. To describe positive results in the latter setting, we use the connections with the theory of singular traces.

We prove a theorem on the existence of solutions of some nonlinear functional integral equations in the Banach algebra of continuous functions on the interval [0,a]. Then we consider a nonlinear in...

In this paper, we consider the existence of solutions for systems of nonlinear p-Laplacian fractional differential equations whose nonlinearity contains the first-order derivative explicity in Banach space E, where 𝜃 is the zero element of E, φp is the p-Laplacian operator, i.e., with p>1, its inverse function is denoted by φq with , and p,q satisfy , is standard Caputo derivative and f:I×E×E→E is continuous. Our main tool is the Sadovskii fixed point theorem.

This paper is concerned with the existence and uniqueness of solution to an initial value problem for a differential equation of variable-order. The results are obtained by means of fixed point theorem. The obtained results are illustrated with the aid of examples.

In this paper, we give some generalization of Darbo’s fixed point theorem related to the measure of noncompactness, and present some results on the existence of coupled fixed point theorem for a special class of operators in a Banach space. Our results generalize and extend some comparable results in the literature. Also as an application, we study the existence of solution for a class of the system of nonlinear functional integral equations. Finally an example illustrating the mentioned applicability is also included.

In this article we study the existence of positive solutions for a dynamic equations on time scales. The main tool employed here is the Schauder’s fixed point theorem. The asymptotic properties of solutions are also treated. The results obtained here extend the work of Dorociakova and Olach (Tatra Mt Math Publ 43:63–70, 2009). Three examples are also given to illustrate this work.

In this paper, we investigate the existence of positive solutions for a nonlinear m-point boundary value problem for the p-Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.

应用不动点定理以及格林函数的性质，在Banach空间中得到了一类带有P-Laplacian算子的分数阶微分方程边值问题解的存在性结果。 The existence of solutions for a class of P-Laplacian fractional differential equation boundary value problem is obtained by means of fixed point theorem and the properties of Green function in Banach Space.

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

In this paper, we establish sufficient conditions for the existence of positive solutions for a class of higher order Riemann–Liouville fractional initial value problems. First, we construct an appropriate Banach space and prove the equivalence between the posed problem and the associated Volterra integral equation, then by means of Guo–Krasnoselskii fixed point theorem, we investigate the existence of at least one positive solution under sublinearity conditions.

The author of the above mentioned paper found that pointwise ergodic theorem for bounded additive processes, cf. Theorem 7.11 needs an additional assumption. Including the assumption of approximability, we show that the ergodic theorem is correct. Since we have not found a proof for Poisson point processes being approximable, we withdraw Corollary 7.12 which stated the pointwise almost-everywhere convergence for those processes. A minor flaw in the proof of the abstract mean ergodic theorem (Theorem 5.7) is fixed as well.

In this paper we prove Caristi’s fixed point theorem using only purely metric techniques.

In this paper, we study a three point boundary value problem of nonlinear fractional differential equations of order α, 2 < α < 3. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii theorems. Some illustrative examples are also presented.

We prove constructively that every uniformly continuous convex function f : X -> R+ has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics. (C) 2016 Elsevier B.V. All rights reserved.

In this paper, we formulate a regular q-fractional Sturm–Liouville problem (qFSLP) which includes the left-sided Riemann–Liouville and the right-sided Caputo q-fractional derivatives of the same order $$\alpha $$ , $$\alpha \in (0,1)$$ . The properties of the eigenvalues and the eigenfunctions are investigated. A q-fractional version of the Wronskian is defined and its relation to the simplicity of the eigenfunctions is verified. We use a fixed point theorem to introduce a sufficient condition on eigenvalues for the existence and uniqueness of the associated eigenfunctions when $$\alpha >1/2$$ . These results are a generalization of the integer regular q-Sturm–Liouville problem introduced by Annaby and Mansour (J Phys A Math Gen 39:8747, 2005). An example for a qFSLP whose eigenfunctions are little q-Jacobi polynomials is introduced.

In this paper we survey a set of Brouwer fixed point theorem equivalents. These equivalents are divided into four loops related to (1) the Borsuk retraction theorem, (2) the Himmelberg fixed point theorem, (3) the Gale lemma and (4) the Nash equilibrium theorem.

Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings S:X×X→X and g:X→X in a bv(s)-metric space, which generalize, extend, and improve some recent results on coupled fixed points. As an application, we prove an existence and uniqueness theorem for the solution of a system of nonlinear integral equations under some weaker conditions and given a convergence criteria for the unique solution, which has been properly verified by using suitable example.

Each one of six general existence principles of compactness (the extreme value theorem), completeness (the Newton method or the modified Newton method), topology (Brouwer’s fixed point theorem), homotopy (on contractions of a sphere to its center), variational analysis (Ekeland’s principle), and monotonicity (the Minty–Browder theorem)) is shown to lead to the inverse function theorem, each one giving some novel insight. There are differences in assumptions and algorithmic properties; some of the propositions have been constructed specially for this paper. Simple proofs of the last two principles are included. The proof by compactness is shorter and simpler than the shortest and simplest known proof, that by completion. This gives a very short self-contained proof of the Lagrange multiplier rule, which depends only on optimization methods. The proofs are of independent interest and are intended as well to be useful in the context of the ongoing efforts to obtain new variants of methods that are based on the inverse function theorem, such as comparative statics methods.

In this paper, we study the complete controllability for a class of non-linear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance. The result is achieved using the Banach fixed-point theorem and Schauder’s fixed-point theorem. Some numerical examples are provided to demonstrate the effectiveness of the main result

We present a variant of an asymptotic version of the Abian-Brown Fixed Point Theorem, and applications to recursively defined sequences and Hammerstein integral equations.