非局部条件下分数阶差分方程边值问题正解的存在性

摘要

This paper studies the existence of positive solution to the discrete fractional boundary value problem(BVP) -△νy(t) =λf(t+ν-1, y(t+ν-1)), y(ν -2) = g1(y), y(ν+b) = g2(y) by giving the summation equation for the solution to this problem, and the eigenvalue intervals and some sufficient conditions for the existence of at least one positive solution to the above problem are established by the Green function and Guo-Krasnosel' skii fixed point theorem on cones.%研究离散分数阶边值问题-Δvy(t)=λf(t+v-1,y(t+v-1)),y(v-2)=g1(y),y(v+b)=g2(y)正解的存在性,通过给出这个问题解的积分表达式,运用Green函数及锥拉伸与压缩不动点定理,得到使上述边值问题至少存在一个正解的特征值区间和一些充分条件.