Fixed-point theorems and difference equations with nonempty set of bounded solutions

DOI10.1007/S10958-019-04237-6zbMath1423.54101OpenAlexW2921911715WikidataQ128219858 ScholiaQ128219858MaRDI QIDQ2313738

V. Yu. Slyusarchuk

Publication date: 23 July 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04237-6

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) General theory of difference equations (39A05) Growth, boundedness, comparison of solutions to difference equations (39A22)

Cites Work

• Exponentially dichotomous difference equations with non-Lipschitz perturbations
• Method of local linear approximation in the theory of bounded solutions of nonlinear difference equations
• Periodic and almost periodic solutions of difference equations in metric spaces
• Method of locally linear approximation of nonlinear difference operators by weakly regular operators
• Invertibility conditions for the nonlinear difference operator \((\mathcal{D}x)(n) = x(n + 1) - f(x(n))\) in the space \(\ell_{\infty}(\mathbb Z, \mathbb R)\)
• On Fixed and Periodic Points Under Contractive Mappings
• Necessary and sufficient conditions for the Lipschitzian invertibility of nonlinear difference operators in the spaces \(\ell_p (\mathbb{Z},\mathbb{R})\) with \(1\leq p\leq\infty\)
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