Infinitely many homoclinic solutions for a class of subquadratic Hamiltonian systems

Abstract

Consider the second order Hamiltonian system: $$\ddot q - L(t)q+ \nabla V(t,q)=0,\eqno (HS)$$ where $V(t,x)=a(t)W(x)$. New results concerning the existence and the multiplicity of  homoclinic solutions to $(HS)$ are obtained in the case where $W$ is of subquadratic growth as $|x| \longrightarrow +\infty$ and the matrix $L(t)$ is positive definite for all $t \in \rb$ without any assumption of periodicity on the potential.