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Existence of \((N, \lambda)\)-periodic solutions for abstract fractional difference equations. (English) Zbl 1484.39010

Summary: We establish sufficient conditions for the existence and uniqueness of \((N, \lambda)\)-periodic solutions for the following abstract model: \[ \Delta^{\alpha} u(n)=Au(n+1)+f(n,u(n)), \quad n\in\mathbb{Z}, \] where \(0 < \alpha \le 1\), \(A\) is a closed linear operator defined in a Banach space \(X\), \(\Delta^{\alpha}\) denotes the fractional difference operator in the Weyl-like sense, and \(f\) satisfies appropriate conditions.

MSC:

39A23 Periodic solutions of difference equations
39A13 Difference equations, scaling (\(q\)-differences)
39A12 Discrete version of topics in analysis
47D06 One-parameter semigroups and linear evolution equations
47D60 \(C\)-semigroups, regularized semigroups
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