Multiple Solutions to Fractional Difference Boundary Value Problems

Abstract

The following fractional difference boundary value problems▵νyt=-ft+ν-1,yt+ν-1,y(ν-2)=y(ν+b+1)=0are considered, where1<ν≤2is a real number and▵νy(t)is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions onfwhich are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results.