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In this paper, we study the existence of positive solutions for a fourth order boundary value problem coupled to functional perturbed clamped beam boundary conditions. Our main ingredient is the classical fixed point index. The problem investigated is an extension of other problems studied in previous papers by covering very general nonlocal perturbed conditions on the boundary. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using fixed point index. We construct a new linear operator and obtain our main results under some conditions concerning the spectral radius of this linear operator. Our method improves and generalizes some results in the literature. [ABSTRACT FROM AUTHOR]

In this work, we investigate a Riemann-Liouville-type impulsive fractional integral boundary value problem. Using the fixed point index, we obtain two existence theorems on positive solutions under some conditions concerning the spectral radius of the relevant linear operator. Our method improves and generalizes some results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with p-Laplacian {(Φp(u"(t)))' + f(t, u(t)) = 0, t (0, 1), u(0) = au(η), u(1) = au(η), u"(0) = 0, is studied, where Φp(s) = |s|p-2s, p > 1. By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application. [ABSTRACT FROM AUTHOR]

We consider the nonlinear conjugate multi-point boundary value problem with feedback control that finds functions $ u $ and $ q $ satisfying$ \begin{align*} & \mathcal Lu(t) = q(t)F[t,u(t),u'(t),..., u^{(m-1)}(t)],\,\, q(t) \in \Phi[t,u(t)],\,\,\, t\in I, \hfill \\ & u^{(j)}(t_i) = 0, \,\,\,\,\, 1\leq i \leq l,\,\,\,\, 0\leq j\leq k_i-1, \hfill \end{align*} $where $ \mathcal L $ is a linear differential operator of order $ m $, $ I = [0,1] $, $ 0 = t_1<...

In this paper, we investigate the positive solutions for Hilfer frac-tional differential equation boundary value problems at resonance. First, we give the expression of the solution with Mittag-Leer function. Next, we ob-tain the existence of the positive solutions by using fixed point index theorem. Finally, we give relevant examples to prove our main results. [ABSTRACT FROM AUTHOR]

In this short note, we prove, by means of classical fixed point index, an affine version of a Birkhoff–Kellogg‐type theorem in cones. We apply our result to discuss the solvability of a class of boundary value problems for functional differential equations subject to functional boundary conditions. We illustrate our theoretical results in an example. [ABSTRACT FROM AUTHOR]

In this paper we use the fixed point index theory to study the existence of positive radial solutions for a system of boundary value problems with semipositone second order elliptic equations. Some appropriate concave and convex functions are utilized to characterize coupling behaviors of our nonlinearities. [ABSTRACT FROM AUTHOR]

In this work a new functional expansion-compression fixed point theorem of Leggett-Williams type is developed for a class of mappings of the form T + F, where (I - T) is Lipschitz invertible map and F is a k -set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem. [ABSTRACT FROM AUTHOR]

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving fractional derivatives. Our analysis methods are based on the fixed point index and nonsymmetric property of the Green function. Additionally, we provide some valid examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China Normal University (Natural Science Edition) / Huanan Shifan Daxue Xuebao (Ziran Kexue Ban) is the property of Journal of South China Normal University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with the existence of positive solutions of the fully fourth-order boundary value pqroblem u (4) = f (t , u , u ′ , u ″ , u ‴) on [ 0 , 1 ] with the boundary condition u (0) = u (1) = u ″ (0) = u ″ (1) = 0 , which models a statically bending elastic beam whose two ends are simply supported, where f : [ 0 , 1 ] × R + × R × R − × R → R + is continuous. Some precise inequality conditions on f guaranteeing the existence of positive solutions are presented. The inequality conditions allow that f (t , u , v , w , z) may be asymptotically linear, superlinear, or sublinear on u , v , w , and z as | (u , v , w , z) | → 0 and | (u , v , w , z) | → ∞ . Our discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones. [ABSTRACT FROM AUTHOR]

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'skiĭ cone compression–expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex set. By iterating this procedure we prove the existence of multiple solutions. We illustrate our theoretical results by applying them to the solvability of systems of Hammerstein integral equations. In the case of two specific boundary value problems and with given nonlinearities, we are also able to obtain a numerical solution, consistent with our theoretical results. [ABSTRACT FROM AUTHOR]

In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under the boundary conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound on the third-order derivative term, and the theory of fixed-point index is used on suitable open sets to obtain the existence of positive solutions. The nonlinearities have quadratic growth in the third-order derivative term. Previous results in the literature are not applicable in our case, as shown by our examples. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the existence of positive solutions for the Hilfer hybrid fractional equation involving a weighted two dimensional φ -Laplacian operator with the integral-infinite point boundary conditions. In this approach, we transform the given fractional differential equation into an equivalent integral equation. Then we establish sufficient conditions and employ the fixed point index arguments to obtain new results on the existence of positive solutions. Examples illustrating the main results are also constructed. This work contains several new ideas, and gives a unified approach applicable to many boundary value problems involving (p,q)-Laplacian type operators. [ABSTRACT FROM AUTHOR]

In this work, we use index fixed point theory for perturbation of expansive mappings by ℓ-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear differential equation on the positive half-line. The nonlinearity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave differently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters: { u (4) (t) + β 1 u ″ (t) − α 1 u (t) = f 1 (t , u (t) , v (t)) , 0 < t < 1 ; v (4) (t) + β 2 v ″ (t) − α 2 v (t) = f 2 (t , u (t) , v (t)) , 0 < t < 1 ; u (0) = u (1) = u ″ (0) = u ″ (1) = 0 ; v (0) = v (1) = v ″ (0) = v ″ (1) = 0 , where f 1 , f 2 ∈ C [ (0 , 1) × R 0 + × R , R ] , R 0 + = (0 , + ∞) . By constructing a special cone and applying fixed point index theory, some new existence results of multiple solutions for the considered system are obtained under some suitable assumptions. Finally, an example is worked out to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence, nonexistence, and multiplicity of positive solutions of the coupled system of Riemann‐Liouville fractional differential equations together with multipoint boundary conditions containing fractional derivatives at nonlocal points. We use the theory of fixed point index approach to prove our results exhibiting the existence and the nonexistence of positive solutions. [ABSTRACT FROM AUTHOR]

New coexistence fixed point theorems in product Banach spaces are established via the classical theory of fixed point index for compact maps defined on cones. Each component of a coexistence fixed point is nonzero. These coexistence fixed point theorems are applied to obtain results on coexistence solutions of systems of Hammerstein integral equations, second‐order ordinary differential equations with general separated boundary conditions, and one‐dimensional competition model of Ricker types. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of population inhabiting a favorable environment surrounded by a region where survival is impossible. We use a parabolic partial differential equation with nonlinearity changing signs to describe the dynamics. By using a recent result on the existence of nonzero fixed point for r-nowhere normal-outward compact maps, we establish new results on existence of nonzero nonnegative or positive steady-state solutions of such boundary value problems. Additionally, we obtain the convergence of positive solutions of such parabolic boundary value problems in the Banach space C 1 , which is different from the previous results that considered weak convergence or uniform convergence. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the positive solutions of beam equations with the nonlinearities including the slope and bending moment under nonlocal boundary conditions involving Stieltjes integrals. We pose some inequality conditions on nonlinearities and the spectral radius conditions on associated linear operators. These conditions mean that the nonlinearities have superlinear or sublinear growth. The existence of positive solutions is obtained by fixed point index on cones in C 2 [ 0 , 1 ] , and some examples are given for beam equations subject to mixed integral and multi-point boundary conditions with sign-changing coefficients. [ABSTRACT FROM AUTHOR]

We discuss the existence and non-existence of non-negative, non-decreasing solutions of certain perturbed Hammerstein integral equations with derivative dependence. We present some applications to nonlinear, second order boundary value problems subject to fairly general functional boundary conditions. The approach relies on classical fixed point index theory. [ABSTRACT FROM AUTHOR]

In this paper we use the fixed point index to study the existence of positive solutions for a system of 2nth-order boundary value problems involving semipositone nonlinearities. [ABSTRACT FROM AUTHOR]

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign chang- ing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results. [ABSTRACT FROM AUTHOR]

In this paper, based on the contraction map principle and the fixed point index theory, sufficient conditions are established for the uniqueness and existence results of positive solution for four-point boundary value problem of nonlinear differential equation with Caputo's fractional order derivative. It is interesting to note that the Krein-Rutmann theorem is also used in this paper. Such investigations will provide an important platform for gaining a deeper understanding of our environment. [ABSTRACT FROM AUTHOR]

This article studies the existence and multiplicity of componentwise positive solutions for systems of nonlinear Hammerstein integral equations. In this system one nonlinear term is uniformly superlinear or uniformly sublinear, and the other is locally uniformly superlinear or locally uniformly sublinear. Discussions are undertaken by means of the fixed point index theory in cones. As applications, we show the existence and multiplicity of component-wise positive solutions for systems of second-order ordinary differential equations with the Dirichlet boundary value conditions and mixed boundary value conditions, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

Abstract We generalize the main result on existence of nonzero nonnegative solutions of systems of second order elliptic boundary value problems obtained by Lan (2011). The motivation for the generalization is to propose and study the competition models of Ricker and Beverton–Holt types governed by such systems. To the best of our knowledge, there is little study on such continuous competition models although such difference equation and first order ordinary differential equation competition models have been widely studied. Our results enrich and develop the connections among the classical fixed point index theory, systems of second order elliptic boundary value problems and population dynamics. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article concerns the boundary value problem consisting of the nonlinear differential equation $$ u''+g(t)f(t,u(t))=0,\quad t\in(0, 1) $$ and the multi-point boundary conditions $$\displaylines{ u(0)=\alpha u'(0), \cr u(1)=\sum_{i=1}^m\beta_iu(\eta_i)+\sum_{i=1}^m\gamma_iu'(\eta_i), }$$ where $0\leq \alpha \leq\infty$, $00$, $\gamma_i

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our knowledge, has never been used before. In order to obtain fixed points of the integral operator, we will consider the fixed point index theory and apply it to this new Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of positive solutions for a system of fourth order p-Laplacian boundary value problems -((-xm)p-1)0 = f(t, x, x', y, y'). t ϵ [0; 1]; -((-ym)p-1)0 = g(t; x; x0; y; y0); t ϵ [0; 1]; x(0) = x'(1) = x"(0) = xm(1) = 0, y(0) = y'(1) = y"(0) = ym(1) = 0, where p > 1, f; g ϵ C([0, 1] ⨰ R+ ⨰ R+ ⨰ R+ ⨰ R+;R+)(R+ := [0;∞)). Under some new general conditions on f and g, we use the fixed point index to establish two existence theorems for the above system. The interesting point lies in the fact that the nonlinear term f; g can be allowed to depend on the first derivative of the unknown functions, and this derivative dependence in systems is seldom considered in the literature. [ABSTRACT FROM AUTHOR]

In this article we establish the exactly determined open interval of positive parameter λ in which the n t h order impulsive singular equation has two infinite families of positive solutions. Noticing that λ > 0 and c k ≠ 0 ( k = 1 , 2 , … , m ) , our main results improve and extend many recent results. Our approach is largely based on the theory of fixed point index, transformation technique and Hölder’s inequality. [ABSTRACT FROM AUTHOR]

This article concerns the existence of positive solutions for p-Laplacian boundary value problem on time scales. By applying fixed point index we obtain the existence of solutions. Emphasis is put on the fact that the nonlinear term is allowed to change sign. An example illustrates our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the second-order problem with dependence on derivative in nonlinearity and Stieltjes integral boundary condition ... where f : [0, 1] × R+ × R+ → R+ is continuous and α[u] is a linear functional. Some inequality conditions on nonlinearity f and the spectral radius conditions of linear operators are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone in C¹[0, 1]. The conditions allow that f (t, x1, x2) has superlinear or sublinear growth in x1, x2. Some examples are given to illustrate the theorems respectively under multi-point and integral boundary conditions with sign-changing coefficients. [ABSTRACT FROM AUTHOR]

We investigate the existence of positive solutions of a system of second-order nonlinear differential equations subject to integral boundary conditions, where the nonlinearities do not possess any sublinear or superlinear growth conditions and may be singular. [ABSTRACT FROM AUTHOR]

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example, when dealing with boundary value problems where nonlocal terms occur in the differential equation and/or in the boundary conditions. Some examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of at least two positive solutions for the following high-order fractional semipositone boundary value problem (SBVP, for short) with coupled integral boundary value conditions:.. where n - 1 < α ≤ n, n ≥ 3, 0 < η1, η2 ≤ 1, λ, λ1, λ2 are parameters and satisfy λ1λ2(η1η2) α < Γ²(α + 1), Dα0+ is the standard Riemann-Liouville derivative, and f, g are continuous and semipositone. By using the nonlinear alternative of Leray-Schauder type, Krasnoselskii's fixed point theorems, and the theory of fixed point index on cone, we establish some existence results of multiple positive solutions to the considered fractional SBVP. As applications, two examples are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a kind of αth $(3<\alpha\leq4)$ order differential equation with two-point boundary conditions is considered. The existence result of a sign-changing solution is given by the topological degree theory and the fixed point index theory. [ABSTRACT FROM AUTHOR]

By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical results, we study some problems that occur in applied mathematics, namely models of chemical reactors, beams and thermostats. We also apply our theory in order to prove the existence of nontrivial radial solutions of systems of elliptic boundary value problems subject to nonlocal, nonlinear boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlocal fractional differential equation: where $1 < \alpha< 2$ , $0 < \xi< 1$ , $\eta\xi^{\alpha-1}= 1$ , $D^{\alpha}_{0+}$ is the standard Riemann-Liouville derivative, $f:[0,1]\times[0,+\infty)\rightarrow\mathbb{R}$ is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique. [ABSTRACT FROM AUTHOR]

We study the existence of positive solutions for some nonlinear second order boundary value problems with nonlocal boundary conditions. The key boundary condition considered is of the form u(1) = α[u'], where a is a linear functional on C[0,1], that is, is given by a Riemann-Stieltjes integral α[v] = ί01 v(s)dA(s) where A is a function of bounded variation. It is important in our case that dA is not a positive measure but can be sign changing. [ABSTRACT FROM AUTHOR]

This paper weals with the existence of positive solutions of the fully second-order boundary value problem [ABSTRACT FROM AUTHOR]

We consider the perturbed Hammerstein equation where φ and ψ are linear functionals, which can be represented as Stieltjes integrals with signed measures, and is a parameter. We demonstrate that by imposing some mild conditions on and , together with an assumption that the functionals decompose in a particular way, it follows that this problem can have multiple positive solutions even if no conditions at all are imposed on f except for a positivity assumption and continuity. Applications are, in particular, given to boundary value problems with nonlocal boundary conditions, and one of these existence results allows to be affine and to be linear. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and multiplicity of positive solutions for a system of nonlinear singular higher-order fractional differential equations with fractional multi-point boundary conditions. The main tool used in the proof is fixed point index theory. Some limit type conditions for ensuring the existence of positive solutions are given, and our conditions are suitable for more general functions. [ABSTRACT FROM AUTHOR]