Publication detail

A precise asymptotic description of half-linear differential equations

ŘEHÁK, P.

English title

A precise asymptotic description of half-linear differential equations

Type

journal article in Web of Science

Language

en

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.

English 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 in English

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

Released

08.04.2024

Publisher

WILEY-V C H VERLAG GMBH

Location

WEINHEIM

ISSN

0025-584X

Volume

297

Number

4

Pages from–to

1275–1309

Pages count

35

BIBTEX


@article{BUT186969,
  author="Pavel {Řehák},
  title="A precise asymptotic description of half-linear differential equations",
  year="2024",
  volume="297",
  number="4",
  month="April",
  pages="1275--1309",
  publisher="WILEY-V C H VERLAG GMBH",
  address="WEINHEIM",
  issn="0025-584X"
}