一类分数阶差分方程正解的存在性

Existence of positive solution for a class of fractional difference equations

研究了一类有限非线性分数阶差分方程边值问题正解的存在性.首先利用分数阶差分方程及其边值条件给出了Green函数,并分析了其性质;然后利用Krasnosel’skii不动点定理,建立了这类分数阶差分方程边值问题正解的存在性定理.

We studied the existence of positive solutions of the boundary value problem for a nonlinear finite fractional difference equation .First ,according to fractional difference equation and its boundary conditions ,we constructed the Green’s function and analyzed its properties .Then ,by using the Krasnosel’skii fixed point theorem we obtained sufficient conditions for the existence of positive solutions of the boundary value problem for the nonlinear finite difference equation .