Positive solutions for a system of fourth-order differential equations with integral boundary conditions and two parameters - Jiang, Ruiting; Zhai, Chengbo (Nonlinear Analysis: Modelling and Control, 2018)
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.
Keywords: integral boundary conditions; two parameters; Green's function; positive solution; Guo–Krasnosel'skii fixed-point theorem