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Publication detail
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
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" }