Asymptotic behavior for a class of damped second-order gradient systems via Lyapunov method

Renan J. S. Isneri, Eric B. Santiago, Severino H. da Silva

In this work we study the asymptotic behavior of a class of damped second-order gradient systems $$\ddot{u}(t)+a\dot{u}(t)+\nabla W(u(t))=0,$$ under assumptions ensuring lo…