Multiple and Nonexistence of Positive Solutions for a Class of Fractional Differential Equations with <i>p</i>-Laplacian Operator

Abstract

Research about multiple positive solutions for fractional differential equations is very important. Based on some outstanding results reported in this field, this paper continue the focus on this topic. By using the properties of the Green function and generalized Avery–Henderson fixed point theorem, we derive three positive solutions of a class of fractional differential equations with a p-Laplacian operator. We also study the nonexistence of positive solutions to the eigenvalue problem of the equation. Three examples are given to illustrate our main result.

Keywords

• positive solutions
• <i>p</i>-Laplacian
• integral boundary conditions
• generalized Avery–Henderson fixed point theorem