Existence of three symmetric positive solutions for a second-order multi-point boundary value problem on time scales

Aycan Sinanoglu,Ilkay Y Karaca,Tugba Senlik,Fatma Tokmak

doi:10.1186/1687-1847-2014-81

Abstract

AbstractIn this article, we investigate the existence of at least three symmetric positive solutions of a second-order multi-point boundary value problem on time scales. The ideas involve Bai and Ge’s fixed point theorem. As an application, we give an example to demonstrate our main result.MSC:34B10, 34B18, 39A10.

Highlights

1 Introduction Calculus on time scales was introduced by Hilger [ ] as a theory which includes both differential and difference calculus as a special cases
Time scale calculus would allow the exploration of a variety of situations in economic, biological, heat transfer, stock market, and epidemic models; see the monographs of Aulbach and Hilger [ ], Bohner and Peterson [, ], and Lakshmikantham et al [ ] and the references therein
The more general nonlinear multi-point boundary value problems have been widely studied by many authors

Summary

Introduction

Calculus on time scales was introduced by Hilger [ ] as a theory which includes both differential and difference calculus as a special cases. The more general nonlinear multi-point boundary value problems have been widely studied by many authors. The existence of symmetric positive solutions of second-order boundary value problems have been studied by some authors, see [ , ].

Results

Conclusion