Detail publikace
On positive periodic solutions to second-order differential equations with a sub-linear non-linearity
LOMTATIDZE, A. ŠREMR, J.
Anglický název
On positive periodic solutions to second-order differential equations with a sub-linear non-linearity
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Klíčová slova anglicky
Periodic solution;second-order differential equation;existence;uniqueness;positive solution
Vydáno
01.02.2021
Nakladatel
Elsevier
Místo
GB - Velká Británie
ISSN
1468-1218
Ročník
2021
Číslo
57
Strany od–do
1–24
Počet stran
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"
}