Publication result detail

Positive periodic solutions to super-linear second-order ODEs

ŠREMR, J.

Original Title

Positive periodic solutions to super-linear second-order ODEs

English Title

Positive periodic solutions to super-linear second-order ODEs

Type

WoS Article

Original Abstract

We study the existence and uniqueness of a positive solution to the problemu ''=p(t)u+q(t,u)u+f(t);u(0)=u(omega),u '(0)=u '(omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u<^>{\prime \prime }} = p(t)u + q(t,u)u + f(t);\,\,\,\,\,u(0) = u(\omega ),\,\,\,{u<^>\prime }(0) = {u<^>\prime }(\omega )$$\end{document}with a super-linear nonlinearity and a nontrivial forcing term f. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.

English abstract

We study the existence and uniqueness of a positive solution to the problemu ''=p(t)u+q(t,u)u+f(t);u(0)=u(omega),u '(0)=u '(omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u<^>{\prime \prime }} = p(t)u + q(t,u)u + f(t);\,\,\,\,\,u(0) = u(\omega ),\,\,\,{u<^>\prime }(0) = {u<^>\prime }(\omega )$$\end{document}with a super-linear nonlinearity and a nontrivial forcing term f. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.

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.

Released

01.03.2025

Publisher

SPRINGER HEIDELBERG

Location

HEIDELBERG

ISBN

0011-4642

Periodical

CZECHOSLOVAK MATHEMATICAL JOURNAL

Volume

75

Number

1

State

Czech Republic

Pages from

257

Pages to

275

Pages count

19

URL

https://link.springer.com/article/10.21136/CMJ.2024.0128-23

BibTex

@article{BUT197721,
  author="Jiří {Šremr}",
  title="Positive periodic solutions to super-linear second-order ODEs",
  journal="CZECHOSLOVAK MATHEMATICAL JOURNAL",
  year="2025",
  volume="75",
  number="1",
  pages="257--275",
  doi="10.21136/CMJ.2024.0128-23",
  issn="0011-4642",
  url="https://link.springer.com/article/10.21136/CMJ.2024.0128-23"
}