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

摘要

The paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problemu′′=p(t)u+q(t,u)u+f(t);u(0)=u(ω), u′(0)=u′(ω),where p,f∈L([0,ω]) and q:[0,ω]×R→R is Carathéodory function. The general results obtained are applied to the forced non-autonomous Duffing equationu′′=p(t)u+h(t)|u|λsgnu+f(t),with λ>1 and a~non-negative h∈L([0,ω]). We allow the coefficient p and the forcing term f to change their signs.