Publication detail

Nonlinear Poincare-Perron theorem

ŘEHÁK, P.

English title

Nonlinear Poincare-Perron theorem

Type

WoS Article

Language

en

Original abstract

We establish a nonlinear extension of the Poincare-Perron theorem for a second order half-linear differential equation. Conditions are established which guarantee that all nontrivial solutions y of the equation are such that a proper limit lim(t ->infinity)y'(t)/y(t) exists. In addition, we discuss establishing precise asymptotic formulae for these solutions. We employ theory of regular variation and thereby, as a by-product, we complete some results for asymptotics of differential equations considered in this framework. The results can serve for comparison purposes involving more general equations and are of importance also from the stability point of view. (C) 2021 Elsevier Ltd. All rights reserved.

Keywords in English

Poincare-Perron theorem; Asymptotic behavior; Half-linear equation

Released

2021-11-01

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISSN

0893-9659

Journal

Applied Mathematics Letters

Volume

121

Number

107425

Pages from–to

1–7

Pages count

7

BIBTEX


@article{BUT176918,
  author="Pavel {Řehák}",
  title="Nonlinear Poincare-Perron theorem",
  journal="Applied Mathematics Letters",
  year="2021",
  volume="121",
  number="107425",
  pages="1--7",
  doi="10.1016/j.aml.2021.107425",
  issn="0893-9659",
  url="https://doi.org/10.1016/j.aml.2021.107425"
}