Detail publikačního výsledku

A note on transformations of independent variable in second order dynamic equations

ŘEHÁK, P.

Originální název

A note on transformations of independent variable in second order dynamic equations

Anglický název

A note on transformations of independent variable in second order dynamic equations

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

The main purpose of this paper is to show how a transformation of independent variable in dynamic equations combined with suitable statements on a general time scale can yield new results or new proofs to known results. It seems that this approach has not been extensively used in the literature devoted to dynamic equations. We present, in particular, two types of applications. In the first one, an original dynamic equation is transformed into a simpler equation. In the second one, a dynamic equation in a somehow critical setting is transformed into a noncritical case. These ideas will be demonstrated on problems from oscillation theory and asymptotic theory of second order linear and nonlinear dynamic equations.

Anglický abstrakt

The main purpose of this paper is to show how a transformation of independent variable in dynamic equations combined with suitable statements on a general time scale can yield new results or new proofs to known results. It seems that this approach has not been extensively used in the literature devoted to dynamic equations. We present, in particular, two types of applications. In the first one, an original dynamic equation is transformed into a simpler equation. In the second one, a dynamic equation in a somehow critical setting is transformed into a noncritical case. These ideas will be demonstrated on problems from oscillation theory and asymptotic theory of second order linear and nonlinear dynamic equations.

Klíčová slova

transformation; chain rule; dynamic equation; time scale; oscillation; asymptotic formulae

Klíčová slova v angličtině

transformation; chain rule; dynamic equation; time scale; oscillation; asymptotic formulae

Autoři

ŘEHÁK, P.

Rok RIV

2021

Vydáno

11.02.2020

Nakladatel

Springer

Místo

Cham

ISBN

978-3-030-35502-9

Kniha

Springer Proceedings in Mathematics & Statistics

Strany od

335

Strany do

353

Strany počet

19

URL

https://link.springer.com/chapter/10.1007/978-3-030-35502-9_15

BibTex

@inproceedings{BUT162130,
  author="Pavel {Řehák}",
  title="A note on transformations of independent variable in second order dynamic equations",
  booktitle="Springer Proceedings in Mathematics & Statistics",
  year="2020",
  number="312",
  pages="335--353",
  publisher="Springer",
  address="Cham",
  doi="10.1007/978-3-030-35502-9\{_}15",
  isbn="978-3-030-35502-9",
  url="https://link.springer.com/chapter/10.1007/978-3-030-35502-9_15"
}