Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian

Abstract

Abstract The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for this problem by means of the Green function and Guo–Krasnoselskii fixed point theorem on cones. Finally, we give some examples to illustrate the use of our results.

Keywords

• Fractional q-difference equations
• Positive solutions
• Boundary value problem
• Guo–Krasnoselskii fixed point theorem