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

作　　者：刘静 费祥历 许晓婕[1] 孙晓雪 

机构地区：[1]中国石油大学(华东)理学院计算与应用数学系,青岛266555

出　　处：《数学理论与应用》2012年第4期33-41,共9页Mathematical Theory and Applications

摘　　要：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.

关 键 词：分数阶微分方程 四点边值问题 正解 锥不动点定理 

分 类 号：O241.8[理学—计算数学]