Publication detail

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

LOMTATIDZE, A. ŠREMR, J.

English title

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

Type

journal article in Web of Science

Language

en

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 in English

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

Released

01.02.2021

Publisher

Elsevier

Location

GB - Velká Británie

ISSN

1468-1218

Volume

2021

Number

57

Pages from–to

1–24

Pages count

24

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",
  year="2021",
  volume="2021",
  number="57",
  month="February",
  pages="1--24",
  publisher="Elsevier",
  address="GB - Velká Británie",
  issn="1468-1218"
}