分数阶微分方程多点边值问题解的存在性

Existence of Solutions for Multi Point Boundary Value Problems for Fractional Differential Equations

利用Leggett-Williams不动点定理,研究了下面这个多点边值问题三个解的存在性,Dα0+u(t)=f(t,u(t),u′(t)),t∈[0,1] u(0)+u′(0)=0,u(1)-m ∑i=1aiu(ξi)=0,这里2≤α≤3,m≥1是整数,0<ξ1<ξ2<…<ξn<1是常数,ai>0,1≤i≤m,并且m∑i=1aiuξα-1i<1,f∈C([0,1]×[0,∞)×[0,∞)→[0,∞)).

In this paper, by employing the Leggett-Williams fixed point theorem, we study the existence of the three solutions for multi point boundary value problem of are integers,O〈ξ1〈ξ2〈…〈ξn〈1 are constants.