Homoclinic solutions for a class of damped vibration systems

Abstract

In this paper, we establish a new existence result on homoclinic solutions for a non periodic damped vibration system
x(t) + q(t)x (t) + V (t; x(t)) = 0;
where q is a continuously dierentiable function and  V (t; x) = K(t; x)+W(t; x). This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the minimax methods.