Publication detail

Nonlinear Poincare-Perron theorem

ŘEHÁK, P.

Original Title

Nonlinear Poincare-Perron theorem

Type

journal article in Web of Science

Language

English

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

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

Authors

ŘEHÁK, P.

Released

1. 11. 2021

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISBN

0893-9659

Periodical

APPLIED MATHEMATICS LETTERS

Year of study

121

Number

107425

State

United States of America

Pages from

1

Pages to

7

Pages count

7

URL

https://doi.org/10.1016/j.aml.2021.107425

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"
}