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Asymptotics of families of solutions of nonlinear difference equations

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Logic and Analysis

Abstract

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.

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  1. Departamento de Matemática, Universidade de Évora, Colégio Luís Verney, Rua Romão Ramalho 59, 7000-671, Évora, Portugal

    Imme P. van den Berg

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  1. Imme P. van den Berg
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Correspondence to Imme P. van den Berg.

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van den Berg, I.P. Asymptotics of families of solutions of nonlinear difference equations. Log Anal 1, 153–185 (2008). https://doi.org/10.1007/s11813-008-0006-0

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  • DOI: https://doi.org/10.1007/s11813-008-0006-0

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