In this article, we discuss a new coupled system of fractional differential equations with integral boundary conditions

In this work, we investigate a class of nonlinear fourth-order systems with coupled integral boundary conditions and two parameters. We give the Green's functions for the system with boundary conditions, and then obtain some useful properties of the Green's functions. By using the Guo-Krasnosel'skii fixed point theorem and the Green's functions, some sufficient conditions for the existence of positive solutions are presented. As applications, two examples are presented to illustrate the application of our main results.

We study a class of nonlocal elliptic equationswith the Dirichlet boundary conditions in bounded domain. Under suitable assumptions on M and the nonlinear term f , the existence and new properties of a unique positive solutions are obtained via a monotone operator method and a mixed monotone operator method.

In this paper, we consider the following nonhomogeneous fractional Schrödinger-Poisson equations:where s, t ∈ (0, 1], 2t + 4s > 3, (-) s denotes the fractional Laplacian. By assuming more relaxed conditions on the nonlinear term f , using some new proof techniques on the verification of the boundedness of Palais-Smale sequence, existence and multiplicity of solutions are obtained.

This work is concerned with sign-changing solutions to the biharmonic equation with Navier boundary conditions. By using the method of invariant sets of descending flow and symmetric mountain pass lemma, we obtain the existence of multiple sign-changing solutions when the nonlinear term is odd.