Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
- Daliang Zhao
- Yansheng Liu
DOIAbstract
This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem DC0+αu(t)=f(t,u(t),u′(t)), 0<t<1, u(1)=u′(1)=u′′(0)=0, where 2<α≤3 is a real number, CD0+α is the Caputo fractional derivative, and f:[0,1]×[0,+∞)×R→[0,+∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii’s fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications,...
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