Detail publikace

A precise asymptotic description of half-linear differential equations

ŘEHÁK, P.

Originální název

A precise asymptotic description of half-linear differential equations

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

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.

Klíčová slova

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

Autoři

ŘEHÁK, P.

Vydáno

8. 4. 2024

Nakladatel

WILEY-V C H VERLAG GMBH

Místo

WEINHEIM

ISSN

0025-584X

Periodikum

Mathematische Nachrichten

Ročník

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

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"
}