Abstract
In this paper, we study the existence of even homoclinic solutions for a damped vibration system
x(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). We use a new kind of superquadratic condition instead of the global Ambrosetti Rabinowitz condition. For the proof we use the Mountain Pass Theorem. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.