Publication detail
Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term
ŠREMR, J.
English title
Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term
Type
journal article in Web of Science
Language
en
Original abstract
We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem u" = p(t)u + h(t)|u|(lambda) sgn u + mu f (t); u(0) = u(omega), u0(0) = u'(omega), where mu is an element of R is a parameter. We assume that p, h, f is an element of L([0, omega]), lambda > 1, and the function h is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term f to change its sign.
English abstract
We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem u" = p(t)u + h(t)|u|(lambda) sgn u + mu f (t); u(0) = u(omega), u0(0) = u'(omega), where mu is an element of R is a parameter. We assume that p, h, f is an element of L([0, omega]), lambda > 1, and the function h is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term f to change its sign.
Keywords in English
Periodic solution; second-order differential equation; existence; Duffing equation; multiplicity; bifurcation; positive solution
Released
05.10.2023
Publisher
Texas State University
Location
SAN MARCOS
ISSN
1072-6691
Volume
2023
Number
65
Pages from–to
1–23
Pages count
23
BIBTEX
@article{BUT185053,
author="Jiří {Šremr},
title="Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term ",
year="2023",
volume="2023",
number="65",
month="October",
pages="1--23",
publisher="Texas State University",
address="SAN MARCOS",
issn="1072-6691"
}