Publication detail

A precise asymptotic description of half-linear differential equations

ŘEHÁK, P.

Original Title

A precise asymptotic description of half-linear differential equations

Type

journal article in Web of Science

Language

English

Original Abstract

We study asymptotic behavior of solutions of nonoscillatory second-order half-linear differential equations. We give (in some sense optimal) conditions that guarantee generalized regular variation of all solutions, where no sign condition on the potential is assumed. For all of these solutions, we establish precise asymptotic formulas, where positive as well as negative potential is considered. We examine, as consequences, also equations with regularly varying coefficients, or with the coefficients viewed as perturbations of exponentials, or the equations under certain critical (double roots) settings. We make also asymptotic analysis of Poincare-Perron solutions. Many of our results are new even in the linear case.

Keywords

asymptotic formula; half-linear differential equation; nonoscillatory solution; Poincare-Perron solution; regular variation

Authors

ŘEHÁK, P.

Released

8. 4. 2024

Publisher

WILEY-V C H VERLAG GMBH

Location

WEINHEIM

ISBN

0025-584X

Periodical

Mathematische Nachrichten

Year of study

297

Number

4

State

Federal Republic of Germany

Pages from

1275

Pages to

1309

Pages count

35

URL

https://onlinelibrary.wiley.com/doi/10.1002/mana.202200302

BibTex

@article{BUT186969,
  author="Pavel {Řehák}",
  title="A precise asymptotic description of half-linear differential equations",
  journal="Mathematische Nachrichten",
  year="2024",
  volume="297",
  number="4",
  pages="1275--1309",
  doi="10.1002/mana.202200302",
  issn="0025-584X",
  url="https://onlinelibrary.wiley.com/doi/10.1002/mana.202200302"
}