Abstract
In this paper, we establish a new existence result on homoclinic solutions for a non periodic damped vibration system
(x) over dot (t) + q(t)(x) over dot (t) V' (t, x(t)) = 0,
where q is a continuously differentiable function and V is an element of C-1 (R x R-N, R), 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.