On existence of positive solutions for a class of discrete fractional boundary value problems
The paper is concerned with the boundary value problem of a fractional difference equation \[ -\Delta^\nu_{\nu-2} u(t) =f(t+\nu-1,u(t+\nu-1)),\quad 1<\nu\leq 2,\quad t\in[0,N+1]\cap\mathbb{N}, \] \[ u(\nu-2)=0,\quad \Delta_{\nu-1}^{\nu-1}u(\nu+N)=0, \] where \(N\geq 2\) is an integer. The paper presents the corresponding Green's function and its properties. Then the Guo-Krasnoselskii fixed point theorem is used to establish the existence of at least one positive solutions of the above BVP.
scientific article; zbMATH DE number 6816291
scientific article