Detail publikace
Asymptotic formulae for solutions of half-linear differential equations
ŘEHÁK, P.
Anglický název
Asymptotic formulae for solutions of half-linear differential equations
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
We establish asymptotic formulae for regularly varying solutions of the half-linear differential equation $$(r(t)|y'|^{\alpha-1}\sgn y')'=p(t)|y|^{\alpha-1}\sgn y,$$ where $r,p$ are positive continuous functions on $[a,\infty)$ and $\alpha\in(1,\infty)$. The results can be understood in several ways: Some open problems posed in the literature are solved. Results for linear differential equations are generalized; some of the observations are new even in the linear case. A refinement on information about behavior of solutions in standard asymptotic classes is provided. A precise description of regularly varying solutions which are known to exist is given. Regular variation of all positive solutions is proved.
Anglický abstrakt
We establish asymptotic formulae for regularly varying solutions of the half-linear differential equation $$(r(t)|y'|^{\alpha-1}\sgn y')'=p(t)|y|^{\alpha-1}\sgn y,$$ where $r,p$ are positive continuous functions on $[a,\infty)$ and $\alpha\in(1,\infty)$. The results can be understood in several ways: Some open problems posed in the literature are solved. Results for linear differential equations are generalized; some of the observations are new even in the linear case. A refinement on information about behavior of solutions in standard asymptotic classes is provided. A precise description of regularly varying solutions which are known to exist is given. Regular variation of all positive solutions is proved.
Klíčová slova anglicky
half-linear differential equation; nonoscillatory solution; regular variation; asymptotic formula
Vydáno
31.01.2017
ISSN
0096-3003
Ročník
292
Strany od–do
165–177
Počet stran
13
BIBTEX
@article{BUT131520,
author="Pavel {Řehák},
title="Asymptotic formulae for solutions of half-linear differential equations",
year="2017",
volume="292",
month="January",
pages="165--177",
issn="0096-3003"
}