分数阶微分方程边值问题的正解

Positive solution for boundary value problems for fractional differential equations

通过运用相应线性算子的第一特征值及其相关性质,以及不动点指数等理论,证明了分数阶微分方程边值问题{D^px(t)+p(t)f(x(t))=0,0<t<1x(0)=x′(0)=0,x(1)=0}至少存在一个正解,其中2<p≤3是一个实数.

In this work, we proved the boundary value problem for fractional differential equation {Dpx（t）＋p（t）f（x（t））=0,0〈t〈1x（0）=x′（0）=0,x（1）=0 eigenvalue of the relevant linear operator and fixed point index theory, where 2〈p≤3 is a real number.