Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions

Abstract

This paper investigates the coupled integral boundary value problem for systems of nonlinear fractional q-difference equations. The nonlinear terms are continuous and semipositone. We firstly give the corresponding Green’s function for the boundary value problem and some of its properties. Moreover, by applying the nonlinear alternative of Leray–Schauder type and Krasnoselskii’s fixed point theorems, we derive an interval of λ such that any λ lying in this interval, the semipositone boundary value problem has one or multiple positive solutions. As applications, some interesting examples are presented to illustrate the main results. Finally, some related boundary value problems are also discussed.