Periodic impact behavior of a class of Hamiltonian oscillators with obstacles

In this paper, we study the existence of harmonic and subharmonic solutions of a class of non-smooth Hamiltonian systems, then apply its results to the vibration problems{−x″=q(x)|x′|2+g(t)x′+f(t),x(t)>0,x′(t0−)=−x′(t0+),ifx(t0)=0. Infinitely many harmonic and subharmonic bouncing solutions are always obtained if q(x)q(x) satisfies some coercive conditions.