Positive solutions for boundary value problems involving nonlinear fractional q-difference equations

Abstract

In this work, we investigate the eigenvalue intervals of nonlinear boundary value prob- lems involving fractional q-difference equations by means of the properties of the Green func- tion and Guo-Krasnosel'skii fixed point theorem on cones. Furthermore, some sufficient condi- tions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As applications, some examples are presented to illustrate the main results.