Detail publikace
On a periodic problem for super-linear second-order ODEs
ŠREMR, J.
Anglický název
On a periodic problem for super-linear second-order ODEs
Typ
Článek WoS
Jazyk
en
Originální abstrakt
The present paper concerns the periodic problemu ''=p(t)u-q(t,u)u+f(t);u(0)=u(omega),u '(0)=u '(omega), $$\begin{array}{} \displaystyle u''=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\, u'(0)=u'(\omega), \end{array}$$where p, f : [0, omega] -> & Ropf; are Lebesgue integrable functions and q : [0, omega] x & Ropf; -> & Ropf; is a Carath & eacute;odory function. We assume that the anti-maximum principle holds for the corresponding linear problem and provide sufficient conditions guaranteeing the existence and uniqueness of a positive solution to the given non-linear problem. The general results obtained are applied to the non-autonomous Duffing type equation with a super-linear power non-linearity.
Klíčová slova anglicky
Second-order differential equation;super-linearity;positive solution;existence; uniqueness
Vydáno
2024-12-15
Nakladatel
WALTER DE GRUYTER GMBH
Místo
BERLIN
ISSN
0139-9918
Ročník
74
Číslo
6
Strany od–do
1457–1476
Počet stran
20
BIBTEX
@article{BUT193694,
author="Jiří {Šremr}",
title="On a periodic problem for super-linear second-order ODEs",
journal="Mathematica Slovaca",
year="2024",
volume="74",
number="6",
pages="1457--1476",
doi="10.1515/ms-2024-0106",
issn="0139-9918",
url="https://www.degruyter.com/document/doi/10.1515/ms-2024-0106/html"
}