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Multiple solutions to fractional difference boundary value problems. (English) Zbl 1469.39002

Summary: The following fractional difference boundary value problems \(\Delta^v y(t)=-f(t+v-1,y(t+v-1))\), \(y(v-2)=y(v+b+1)=0\) are considered, where \(1<v\leq 2\) is a real number and \(\Delta^v y(t)\) is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiĭ theorem and the Schauder fixed point theorem, we establish some conditions on \(f\) which 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.

MSC:

39A12 Discrete version of topics in analysis
34A08 Fractional ordinary differential equations
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