Publication detail

Bifurcation of positive periodic solutions to non-autonomous undamped Duffing equations

ŠREMR, J.

Original Title

Bifurcation of positive periodic solutions to non-autonomous undamped Duffing equations

Type

journal article in Scopus

Language

English

Original Abstract

We study a bifurcation of positive solutions to the parameter-dependent periodic problem u''=p(t)u−h(t)|u|^λ sgn u+µf(t); u(0)=u(ω), u'(0)=u'(ω), where λ>1, p, h, f∈L([0, ω]), and µ∈R is a parameter. Both the coefficient p and the forcing term f may change their signs, h≥0 a. e. on [0, ω]. We provide sharp conditions on the existence and multiplicity as well as non-existence of positive solutions to the given problem depending on the choice of the parameter µ.

Keywords

periodic solution;second-order differential equation;Duffing equation;existence;multiplicity;bifurcation;positive solution

Authors

ŠREMR, J.

Released

29. 6. 2021

Publisher

Institute of Mathematics, Brno University of Technology

Location

Česká republika

ISBN

1805-3610

Periodical

Mathematics for applications

Year of study

10

Number

1

State

Czech Republic

Pages from

79

Pages to

92

Pages count

14

URL

http://ma.fme.vutbr.cz/10_1.html

BibTex

@article{BUT171908,
  author="Jiří {Šremr}",
  title="Bifurcation of positive periodic solutions to non-autonomous undamped Duffing equations",
  journal="Mathematics for applications",
  year="2021",
  volume="10",
  number="1",
  pages="79--92",
  doi="10.13164/ma.2021.07",
  issn="1805-3610",
  url="http://ma.fme.vutbr.cz/10_1.html"
}