NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 47, Issue 1, 2010, pp.81-87
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2010.47.1.081

Title & Authors

NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

Guo, Yingxin;

Guo, Yingxin;

Abstract

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) , 0 < t < 1 u(0) = u(1) = 0, where > 0 is a parameter, 1 < 2, is the standard Riemann-Liouville differentiation, f : [0, 1] is continuous, and q(t) : (0, 1) [0, ] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

Keywords

standard Riemann-Liouville differentiation;fractional differential equation;boundary-value problem;nontrivial solution;Leray-Schauder nonlinear alternative;

Language

English

Cited by

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