Publication result detail

On a periodic problem for super-linear second-order ODEs

ŠREMR, J.

Original Title

On a periodic problem for super-linear second-order ODEs

English Title

On a periodic problem for super-linear second-order ODEs

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

Second-order differential equation;super-linearity;positive solution;existence; uniqueness

Key words in English

Second-order differential equation;super-linearity;positive solution;existence; uniqueness

Authors

ŠREMR, J.

RIV year

2025

Released

15.12.2024

Publisher

WALTER DE GRUYTER GMBH

Location

BERLIN

ISBN

0139-9918

Periodical

Mathematica Slovaca

Volume

74

Number

6

State

Slovak Republic

Pages from

1457

Pages to

1476

Pages count

20

URL

https://www.degruyter.com/document/doi/10.1515/ms-2024-0106/html

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"
}