Detail publikace

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

ŠREMR, J.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

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

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

Autoři

ŠREMR, J.

Vydáno

15. 12. 2024

Nakladatel

WALTER DE GRUYTER GMBH

Místo

BERLIN

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Ročník

74

Číslo

6

Stát

Slovenská republika

Strany od

1457

Strany do

1476

Strany počet

20

URL

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"
}