一个分数阶微分方程四点边值问题正解的存在性

Existence of Positive Solutions for Four Points Boundary Value Problems of a Nonlinear Fractional Differential Equation

本文研究下面的分数阶微分方程四点边值问题Dα0+u(t)+f(t,u(t))=0,0<t<1u'(0)-βu(ξ)=0,u'(1)+γu(η)=0,u″(0)={0正解的存在性,这里2<α≤3,t,s∈[0,1),1≤p≤+∞,1p+1q=1是Caputo分数阶导数,t|→Kt:[0,1]→Lp[0,1],λ.借助于格林函数的性质,应用锥拉伸和锥压缩不动点定理给出了一个正解的存在性定理.

In this paper, the propertis of the Green function is discussed, the existence of of positive solution for four points boundary value problems of a nonlinear fractionaldifferential equation are obtained, where 2 〈 α≤ 3,0 ≤ξ≤η≤1,0≤β, γ≤1,D0n is the standard Caputo differentiation.