Publication detail

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

ŠREMR, J.

English title

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

Type

WoS Article

Language

en

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.

Keywords in English

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

Released

2024-12-15

Publisher

WALTER DE GRUYTER GMBH

Location

BERLIN

ISSN

0139-9918

Volume

74

Number

6

Pages from–to

1457–1476

Pages count

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"
}