Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

Xiaoling Han,Hongliang Gao

doi:10.1155/2011/725494

Abstract

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation are considered, where 1 < α ≤ 2 is a real number, λ is a positive parameter, is the standard Riemann‐Liouville differentiation, and ξi ∈ (0,1), αi ∈ [0, ∞) with , a(t) ∈ C([0,1], [0, ∞)), f(t, u) ∈ C([0, ∞), [0, ∞)).

Highlights

Fractional differential equations have been of great interest recently
Many results were obtained dealing with the existence and multiplicity of solutions of nonlinear fractional differential equations by the use of techniques of nonlinear analysis, see 7–21 and the reference therein
Bai and Lu 7 studied the existence of positive solutions of nonlinear fractional differential equation

Summary

Introduction

Fractional differential equations have been of great interest recently. This is caused both by the intensive development of the theory of fractional calculus itself and by the applications of such constructions in various sciences such as physics, mechanics, chemistry, and engineering. By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation Σ∞i 1αiu ξi are considered, where 1 < α

Results

Conclusion