Existence of multiple positive solutions for third-order p-Laplacian functional dynamic equations on time scales

Wen Guan

doi:10.1186/1687-1847-2014-242

Abstract

In this paper, we consider a class of boundary value problems for third-order p-Laplacian functional dynamic equations on time scales, some existence criteria of at least three positive solutions are established. The main tool used in this paper is the fixed point theorem due to Avery and Peterson (Comput. Math. Appl. 42:313-322, 2001).

Highlights

Some authors have paid much attention to the existence of positive solutions for functional dynamic equations on time scales [ – ], especially for the p-Laplacian functional dynamic equations on time scales [, – ]
In [ ], Wang and Guan considered the existence of positive solutions to problem ( . )
⎨ui(t), ⎩φ(t), t ∈ [ , T]T, i = , , , t ∈ [–r, ]T, which are three positive solutions of BVP

Summary

Introduction

Some authors have paid much attention to the existence of positive solutions for functional dynamic equations on time scales [ – ], especially for the p-Laplacian functional dynamic equations on time scales [ , – ]. In [ ], Kaufmann and Raffoul considered a nonlinear functional dynamic equation on time scales and obtained sufficient conditions for the existence of positive solutions. In [ ], by using a double fixed point theorem due to Avery et al [ ], Song and Gao considered the existence of at least twin positive solutions to the following p-Laplacian functional dynamic equations on time scales:

Results

Conclusion