分数阶微分方程多点边值问题正解的存在性

Existence of Positive Solutions for Multi-point Boundary Value Problems of Fractional Differential Equations

讨论了一类分数阶微分方程的多点边值问题D^(ν)_(0+)u(t)+h(t)f(u(t))=0,0<t<1,n-1<ν≤n,ν>3,u(0)=u′(0)=u″(0)=…=u^((n-2))(0)=0,n≥3,(D^(α)_(0+)u(t))t=1=∑m-2i=1β_(i)(D^(α)_(0+)u(t))_(t=η_(i)),1≤α≤n-2.其中η_(i)∈(0,1),0<η_(1)<η_(2)<…<η_(m-2)<1,β_(i)∈[0,+∞)。研究该问题的格林函数及其相关性质,运用凸泛函不动点指数定理来计算不动点指数,从而得到了该问题正解的存在性。