Convergence of Solutions of Second-Order Gradient-Like Systems with Analytic Nonlinearities

We consider the second-order gradient-like systemUtt+g(Ut)= F(U) (1)whereF: N→ is analytic andg: N→ Nis Lipschitz and coercive withg(0)=0. We prove the convergence of global and bounded solutions of (1) to some equilibrium points.