Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters

Ying Wang,Yonghong Wu,Lishan Liu

doi:10.1186/1687-1847-2014-268

Abstract

Abstract In this paper, we study the existence of a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters. By using the properties of the Green’s function and the Guo-Krasnosel’skii fixed point theorem, we obtain some existence results of positive solutions under some conditions concerning the nonlinear functions. The method of this paper is a unified method for establishing the existence of positive solutions for a large number of nonlinear differential equations with coupled boundary conditions. In the end, examples are given to demonstrate the validity of our main results. MSC:34B16, 34B18.

Highlights

1 Introduction Coupled boundary conditions arise in the study of reaction-diffusion equations, SturmLiouville problems, mathematical biology and so on; see [ – ]
In [ ], Yang considered the positive solutions to boundary values problem for a coupled system of nonlinear fractional differential equations as follows:
By applying the Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed point theorems of cone expansion and compression of norm type, sufficient conditions for the existence and nonexistence of positive solutions to a general class of integral boundary value problems for a coupled system of fractional differential equations are obtained

Summary

Introduction

Coupled boundary conditions arise in the study of reaction-diffusion equations, SturmLiouville problems, mathematical biology and so on; see [ – ]. By using the Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solutions are obtained. In [ ], Yang considered the positive solutions to boundary values problem for a coupled system of nonlinear fractional differential equations as follows:

Results

Conclusion