On Ground-State Homoclinic Orbits of a Class of Superquadratic Damped Vibration Systems

In this paper, we are interested in the following damped vibration system: (t) + q(t)u(t) + Bu(t) + 1/2 q(t)Bu(t) - L(t)u(t) + del W(t, u(t)) = 0, (1) where B is an antisymmetric N x N constant matrix, q : R -> R is a continuous function, L(t) is an element of C(R, R-N2) is a symmetric matrix, and W(t, x) is an element of C-1 (R x R-N, R) are neither autonomous nor periodic in t. The novelty of this paper is that, supposing that Q(t) = integral(t)(0) q(s) ds is bounded from below and L(t) is coercive unnecessarily uniformly positively definite for all t. R, we establish the existence of ground-state homoclinic solutions for (1) when the potential W(t, x) satisfies a kind of superquadratic conditions due to Ding and Luan for Schrodinger equation. The main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. Some recent results in the literature are generalized and significantly improved.