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 WoS

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.

Klíčová slova anglicky

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

Vydáno

2017-01-31

ISSN

0096-3003

Časopis

APPLIED MATHEMATICS AND COMPUTATION

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",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2017",
  volume="292",
  pages="165--177",
  doi="10.1016/j.amc.2016.07.020",
  issn="0096-3003",
  url="http://www.sciencedirect.com/science/article/pii/S0096300316304581"
}