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

Haoran Zhang, Zhaocai Hao () and Martin Bohner
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Haoran Zhang: School of Mathematical Sciences, Qufu Normal University, Jining 273165, China
Zhaocai Hao: School of Mathematical Sciences, Qufu Normal University, Jining 273165, China
Martin Bohner: Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA

Mathematics, 2024, vol. 12, issue 23, 1-14

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; p -Laplacian; integral boundary conditions; generalized Avery–Henderson fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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