Publication result detail

Necessary and sufficient conditions of disconjugacy for the fourth order linear ordinary differential equations

MUKHIGULASHVILI, S.; MANJIKASHVILI, M.

Original Title

Necessary and sufficient conditions of disconjugacy for the fourth order linear ordinary differential equations

English Title

Necessary and sufficient conditions of disconjugacy for the fourth order linear ordinary differential equations

Type

WoS Article

Original Abstract

We study the disconjugacy of the fourth order linear ordinary differential equation u(4)(t) = p(t)u(t); on the interval [a; b]: We find necessary and sufficient conditions for the disconjugacy on [a; b], which have the comparison theorems character. Our results complete Kondrat'ev's second comparison theorem for the case of the fourth order ODE. The above mentioned conditions significantly improve Coppel's well-known condition which guarantees the disconjugacy of our equation for not necessarily constant sign coefficient p; and generalise some optimal disconjugacy results proved for constant-coefficient equations.

English abstract

We study the disconjugacy of the fourth order linear ordinary differential equation u(4)(t) = p(t)u(t); on the interval [a; b]: We find necessary and sufficient conditions for the disconjugacy on [a; b], which have the comparison theorems character. Our results complete Kondrat'ev's second comparison theorem for the case of the fourth order ODE. The above mentioned conditions significantly improve Coppel's well-known condition which guarantees the disconjugacy of our equation for not necessarily constant sign coefficient p; and generalise some optimal disconjugacy results proved for constant-coefficient equations.

Keywords

Disconjugacy, necessary and sufficient conditions, comparison theorem, 4th order ordinary differential equations.

Key words in English

Disconjugacy, necessary and sufficient conditions, comparison theorem, 4th order ordinary differential equations.

Authors

MUKHIGULASHVILI, S.; MANJIKASHVILI, M.

RIV year

2022

Released

20.09.2021

ISBN

1220-3874

Periodical

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie

Volume

2021

Number

4

State

Romania

Pages from

341

Pages to

353

Pages count

13

URL

http://www.rmi.ge/eng/QUALITDE-2021/Mukhigulashvili_workshop_2021.pdf

BibTex

@article{BUT172903,
  author="Sulkhan {Mukhigulashvili} and Mariam {Manjikashvili}",
  title="Necessary and sufficient conditions of disconjugacy for the fourth order linear ordinary differential equations",
  journal="Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie",
  year="2021",
  volume="2021",
  number="4",
  pages="341--353",
  issn="1220-3874",
  url="http://www.rmi.ge/eng/QUALITDE-2021/Mukhigulashvili_workshop_2021.pdf"
}