We determine eigenvalue intervals of λ1 and λ2 for the existence of at least one positive solution for a coupled system of Riemann–Liouville type multi-point fractional order boundary value problems by utilizing a fixed point theorem on a cone under suitable conditions.

In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integrodifferential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.

In this paper, we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal cqnditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer’s fixed-point theorem. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Existence theorem, Delay integrodifferential eq...

In the article, a nonlocal boundary value problem has been investigated for fourth-order mixed-type equation degenerating inside and on of domain. Applying method separation variables to under study, spectral an ordinary differential is obtained. The Green function last constructed, with help which it equivalently reduced Fredholm integral second kind symmetric kernel, implies existence eigenva...

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both q+(t) and q−(t) in addition to that of |q(t)|. The Green’s function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of sol...

We study the existence of nonnegative solutions for second order nonlinear differential systems with periodic boundary conditions. In this class of problems, where the associated Green’s function may take on negative values, and the nonlinear term is allowed to be singular. Our method is based on the Guo-Krasnosel’skii fixed point theorem of cone expansion and compression type, involving a new ...