分数阶半正边值问题一个正解的存在性定理

摘要

考虑分数阶半正边值问题：Dα0+u(t)=λf (t,u(t)),0< t <1, u(0)=u(1)=u′(0)=u′(1)=0正解的存在性。其中：3<α≤4是一个实数；D没有数值下界。应用 Krasnosel’skii 不动点定理证明该方程一个正解的存在性。%We studied a positive solution of the semipositone boundary value problem of fractional differential equation:Dα0+u(t)=λf (t,u(t)), 0 < t < 1, u(0)=u(1)=u′(0)=u′(1)=0, where 3<α≤4 is a real number,and Dα0+ is the standard Riemann-Liouville differentiation,and the nonlinear term has no numerical lower bound.We gave an existence theorem of this equation by means of the Krasnosel’skii fixed-point theorem on a cone.