A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.

In this paper we study the existence of subharmonic solutions of the hamiltonian system$$J\dot{x}+u^{*}\nabla G(t,u\left(x\right))=e\left(t\right)$$where $u$ is a linear map, $G$ is a $C^1$-function and $e$ is a continuous function.

In this paper we study the existence of subharmonic solutions of the Hamiltonian system $$J\dot{x}+u^{*}\nabla G(t,u\left(x\right))=e\left(t\right)$$ where u is a linear map, G is a C1-function and e is a continuous function.