Asymptotic behavior of solutions to difference equations in Banach spaces

We investigate the asymptotic properties of solutions to higher order nonlinear difference equations in Banach spaces. We introduce a new technique based on a vector version of discrete L’Hospital’s rule, remainder operator, and the regional topology on the space of all sequences on a given Banach s...

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Bibliographic Details
Main Author: Migda Janusz
Format: Serial
Published: 2021
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet, Banach tér
Subjects:
doi:10.14232/ejqtde.2021.1.88

Online Access:http://acta.bibl.u-szeged.hu/75809
Description
Summary:We investigate the asymptotic properties of solutions to higher order nonlinear difference equations in Banach spaces. We introduce a new technique based on a vector version of discrete L’Hospital’s rule, remainder operator, and the regional topology on the space of all sequences on a given Banach space. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we are dealing with the problem of approximation of solutions. Our technique allows us to control the degree of approximation of solutions.
Physical Description:17
ISSN:1417-3875