Publication detail

Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations

ŠREMR, J.

Original Title

Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations

Type

journal article in Web of Science

Language

English

Original Abstract

The paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problem u''=p(t)u+q(t,u)u+f (t); u(0)=u(\omega), u'(0)=u'(\omega), where p, f\in L([0,\omega]) and q : [0,\omega]\times R\to R is Carathéodory function. Obtained general results are applied to the forced non-autonomous Duffing equation u'' = p(t)u+h(t)|u|^\lambda\sgn u+f (t), with \lambda>1 and a non-negative h\in L([0,\omega]). We allow the coefficient p and the forcing term f to change their signs.

Keywords

Positive periodic solution;second-order differential equation;Duffing equation;existence;uniqueness;multiplicity

Authors

ŠREMR, J.

Released

8. 9. 2021

Publisher

Bolyai Institute, University of Szeged

Location

Hungary

ISBN

1417-3875

Periodical

Electronic Journal of Qualitative Theory of Differential Equations

Year of study

2021

Number

62

State

Hungary

Pages from

1

Pages to

33

Pages count

33

URL

http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9185

Full text in the Digital Library

http://hdl.handle.net/11012/201678

BibTex

@article{BUT172441,
  author="Jiří {Šremr}",
  title="Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations",
  journal="Electronic Journal of Qualitative Theory of Differential Equations",
  year="2021",
  volume="2021",
  number="62",
  pages="1--33",
  doi="10.14232/ejqtde.2021.1.62",
  issn="1417-3875",
  url="http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9185"
}