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

journal article in Web of Science

en

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.

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.

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

08.09.2021

Bolyai Institute, University of Szeged

Hungary

1417-3875

2021

62

1–33

33