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"
}