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"
}