Publication result detail

ON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

OPLUŠTIL, Z.

Original Title

ON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

English Title

ON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

Type

WoS Article

Original Abstract

The paper studies the non-oscillatory properties of two-dimensional systems of non-linear differential equations u ' = g(t)|v|1/alpha sgn v, v ' = -p(t)|u|(alpha)sgn u, where the functions g: [0, +infinity[-> [0, +infinity[, p: [0, +infinity[-> & Ropf; are locally integrable and alpha > 0. We are especially interested in the case of integral(+infinity)g(s) ds < +infinity. In the paper, new non-oscillation criteria are established. Among others, they generalize well-known results for linear systems as well as second order linear and also half-linear differential equations. The criteria presented complement the results of Hartman-Wintner's type for the system in question.

English abstract

The paper studies the non-oscillatory properties of two-dimensional systems of non-linear differential equations u ' = g(t)|v|1/alpha sgn v, v ' = -p(t)|u|(alpha)sgn u, where the functions g: [0, +infinity[-> [0, +infinity[, p: [0, +infinity[-> & Ropf; are locally integrable and alpha > 0. We are especially interested in the case of integral(+infinity)g(s) ds < +infinity. In the paper, new non-oscillation criteria are established. Among others, they generalize well-known results for linear systems as well as second order linear and also half-linear differential equations. The criteria presented complement the results of Hartman-Wintner's type for the system in question.

Keywords

two dimensional system of non-linear differential equations; oscillatory properties

Key words in English

two dimensional system of non-linear differential equations; oscillatory properties

Authors

OPLUŠTIL, Z.

RIV year

2025

Released

28.11.2024

Publisher

UNIV MISKOLC INST MATH

Location

MISKOLC

ISBN

1787-2413

Periodical

Miskolc Mathematical Notes

Volume

25

Number

2

State

Hungary

Pages from

943

Pages to

954

Pages count

13

URL

https://real.mtak.hu/210795/

Full text in the Digital Library

http://hdl.handle.net/11012/250883

BibTex

@article{BUT194057,
  author="Zdeněk {Opluštil}",
  title="ON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS",
  journal="Miskolc Mathematical Notes",
  year="2024",
  volume="25",
  number="2",
  pages="943--954",
  doi="10.18514/MMN.2024.4420",
  issn="1787-2405",
  url="https://real.mtak.hu/210795/"
}

Documents

4420