Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system

This paper deals with existence and exponential decay of homoclinic orbits in the first-order Hamiltonian systemz˙=JHz(t,z) where the Hamiltonian function H(t,z)H(t,z) is nonperiodic in t∈Rt∈R and superquadratic in z∈R2Nz∈R2N. With certain mild conditions we obtain the solutions via variational methods for strongly indefinite problems.