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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References:

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