一类分数阶微分方程周期边值问题正解的存在性

Existence of Positive Solutions to Periodic Boundary Value Problems for a Class of Fractional Differential Equations

运用Krasnosel’skii不动点定理研究了分数阶微分方程周期边值问题{D0^α+u(t)-λu(t)=μf(t,t^1-αu(t)),0<t≤1,limt→0+t^1-αu(t)=u(1),0<α≤1正解的存在性.其中λ<0,μ>0,Dα0+u是u(t)的Riemann-Liouville分数阶微分,f∶(0,1]×[0,+∞)→[0,+∞)为连续函数.

This paper studies the existence of nonnegative solutions to periodic boundary value problems of fractional differential equations by means of Krasnosel’skii fixed-point theorem,{D0^α+u(t)-λu(t)=μf(t,t^1-αu(t)),0<t≤1,lim t→0+t^1-αu(t)=u(1),0<α≤1 Where λ<0,μ>0,Dα0+u is the Riemann-Liouville fractional derivative of u(t),f∶(0,1]×[0,+∞)→[0,+∞)is a continuous function.