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 ′ ( t 0 − ) = − x ′ ( t 0 + ) , if x ( t 0 ) = 0 . Infinitely many harmonic and subharmonic bouncing solutions are always obtained if q ( x ) satisfies some coercive conditions.