Publication detail

Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes

ŘEHÁK, P.

English title

Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes

Type

journal article in Web of Science

Language

en

Original abstract

We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications regarding asymptotics of solutions. We focus on an exhaustive analysis of the relations among several types of classes which include the classes constructed with respect to the values of the limits of solutions and their quasiderivatives, the classes of regularly varying solutions, the classes of principal and nonprincipal solutions, and the classes of the so-lutions that obey certain asymptotic formulae. Many of our observations are new even in the case of linear differential equations, and we provide also the revision of existing results.

English abstract

We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications regarding asymptotics of solutions. We focus on an exhaustive analysis of the relations among several types of classes which include the classes constructed with respect to the values of the limits of solutions and their quasiderivatives, the classes of regularly varying solutions, the classes of principal and nonprincipal solutions, and the classes of the so-lutions that obey certain asymptotic formulae. Many of our observations are new even in the case of linear differential equations, and we provide also the revision of existing results.

Keywords in English

half-linear differential equationregularly varying functionprincipal solu-tionasymptotic formula

Released

03.01.2023

Publisher

Bolyai Institute, University of Szeged

ISSN

1417-3875

Volume

2023

Number

1

Pages from–to

1–28

Pages count

28

BIBTEX


@article{BUT183067,
  author="Pavel {Řehák},
  title="Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes",
  year="2023",
  volume="2023",
  number="1",
  month="January",
  pages="1--28",
  publisher="Bolyai Institute, University of Szeged",
  issn="1417-3875"
}