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

Abstract

We study a bifurcation of positive solutions to the parameter-dependentperiodic problem u′′=p(t)u−h(t)|u|λsgnu+μf(t);u(0) =u(ω), u′(0) =u′(ω),whereλ >1,p,h,f∈L([0,ω]), andμ∈Ris a parameter. Both the coefficientpand the forcing termfmay change their signs, h≥0a. e. on[0,ω]. We providesharp conditions on the existence and multiplicity as well as non-existence of positivesolutions to the given problem depending on the choice of the parameter μ.