Fast homoclinic solutions for a class of damped vibration problems with subquadratic potentials

In this paper, we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problems (u) over dot(t) + q(t)(u) over dot(t) - L(t)u(t) + del W(t, u(t)) = 0, where L(t) andW(t, x) are neither autonomous nor periodic in t. Our approach is variational and it is based on the critical point theory. We prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function. Our theorems appear to be the first such result and our results extend some recent works. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim