Multiplicity of positive solutions for Sturm-Liouville boundary value problems of fractional differential equations with p-Laplacian
School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, P.R. China
Boundary Value Problems 2014, 2014:26 doi:10.1186/1687-2770-2014-26Published: 30 January 2014
In this article, we investigate the Sturm-Liouville boundary value problems of fractional differential equations with p-Laplacian
where , , , are the standard Caputo fractional derivatives, , , , , , , and is continuous. By means of the properties of the Green’s function, Leggett-Williams fixed-point theorems, and fixed-point index theory, several new sufficient conditions for the existence of at least two or at least three positive solutions are obtained. As an application, an example is given to demonstrate the main result.
MSC: 34A08, 34B18, 35J05.