In this paper we study the existence and multiplicity of homoclinic solutions
for the second order Hamiltonian system u¨−L(t)u(t)+Wu​(t,u)=0,
∀t∈R, by means of the minmax arguments in the critical
point theory, where L(t) is unnecessary uniformly positively definite for all
t∈R and Wu​(t,u) sastisfies the asymptotically linear
condition.Comment: published in International Mathematical Forum, Vol. 6, 2011, no. 4,
159 - 17