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

článek v časopise ve Scopus, Jsc

en

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.

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.

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

29.06.2021

Institute of Mathematics, Brno University of Technology

Česká republika

1805-3610

10

1

79–92

14