Existence of Positive Solutions for Singular Fourth Order Coupled System with Sign Changing Nonlinear Terms

Abstract

This paper deals with the existence of positive solutions to a singular fourth order coupled system with integral boundary conditions. Since the nonlinear terms $f$, $g$ may change sign or be singular at $t = 0$ or $t = 1$, the authors make a priori estimates to overcome some difficulties and apply Guo-Krasnoselskii fixed point theorem to prove the existence of solutions of the system under suitable assumptions. Finally, some examples to illustrate the main results are given.