Detail publikačního výsledku

A precise asymptotic description of half-linear differential equations

ŘEHÁK, P.

Originální název

A precise asymptotic description of half-linear differential equations

Anglický název

A precise asymptotic description of half-linear differential equations

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŘEHÁK, P.

Rok RIV

2025

Vydáno

08.04.2024

Nakladatel

WILEY-V C H VERLAG GMBH

Místo

WEINHEIM

ISSN

0025-584X

Periodikum

Mathematische Nachrichten

Svazek

297

Číslo

4

Stát

Spolková republika Německo

Strany od

1275

Strany do

1309

Strany počet

35

URL

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

Plný text v Digitální knihovně

http://hdl.handle.net/11012/245540

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"
}