Publication result detail

On positive periodic solutions to second-order differential equations with a sub-linear non-linearity

LOMTATIDZE, A.; ŠREMR, J.

Original Title

On positive periodic solutions to second-order differential equations with a sub-linear non-linearity

English Title

On positive periodic solutions to second-order differential equations with a sub-linear non-linearity

Type

WoS Article

Original Abstract

The paper studies the existence and uniqueness of a positive periodic solution to the equation u′′ = p(t)u − q(t, u), where p ∈ L([0, ω]) and q : [0, ω] × R → R is a Carathéodory function sub-linear in the second argument. The general results are applied to some particular cases such as the equation u′′ = p(t)u − h(t) sin u with p, h ∈ L([0, ω]). This equation appears when approximating non-linearities in the equation of motion of a certain non-linear oscillator, namely, a pendulum deflected towards the two charged bodies.

English abstract

The paper studies the existence and uniqueness of a positive periodic solution to the equation u′′ = p(t)u − q(t, u), where p ∈ L([0, ω]) and q : [0, ω] × R → R is a Carathéodory function sub-linear in the second argument. The general results are applied to some particular cases such as the equation u′′ = p(t)u − h(t) sin u with p, h ∈ L([0, ω]). This equation appears when approximating non-linearities in the equation of motion of a certain non-linear oscillator, namely, a pendulum deflected towards the two charged bodies.

Keywords

Periodic solution;second-order differential equation;existence;uniqueness;positive solution

Key words in English

Periodic solution;second-order differential equation;existence;uniqueness;positive solution

Authors

LOMTATIDZE, A.; ŠREMR, J.

RIV year

2021

Released

01.02.2021

Publisher

Elsevier

Location

GB - Velká Británie

ISBN

1468-1218

Periodical

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Volume

2021

Number

57

State

Kingdom of the Netherlands

Pages from

1

Pages to

24

Pages count

24

URL

https://www.sciencedirect.com/science/article/pii/S1468121820301188?via%3Dihub

BibTex

@article{BUT165693,
  author="Aleksandre {Lomtatidze} and Jiří {Šremr}",
  title="On positive periodic solutions to second-order differential equations
with a sub-linear non-linearity",
  journal="NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS",
  year="2021",
  volume="2021",
  number="57",
  pages="1--24",
  doi="10.1016/j.nonrwa.2020.103200",
  issn="1468-1218",
  url="https://www.sciencedirect.com/science/article/pii/S1468121820301188?via%3Dihub"
}