Publication detail

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

ŘEHÁK, P.

Original Title

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

English Title

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

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

11.02.2020

Publisher

Springer

Location

Cham

ISBN

978-3-030-35502-9

Book

Springer Proceedings in Mathematics & Statistics

Edition number

312

Pages from

335

Pages to

353

Pages count

19

URL

BibTex


@inproceedings{BUT162130,
  author="Pavel {Řehák}",
  title="A note on transformations of independent variable in second order dynamic equations",
  annote="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.
",
  address="Springer",
  booktitle="Springer Proceedings in Mathematics & Statistics",
  chapter="162130",
  doi="10.1007/978-3-030-35502-9_15",
  howpublished="online",
  institution="Springer",
  year="2020",
  month="february",
  pages="335--353",
  publisher="Springer",
  type="conference paper"
}