Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

Abstract EN

This paper concerns solutions for the Hamiltonian system: z˙=?Hz(t,z).

Here H(t,z)=(1/2)z⋅Lz+W(t,z), L is a 2N×2N symmetric matrix, and W∈C1(ℝ×ℝ2N,ℝ).

We consider the case that 0∈σc(−(?(d/dt)+L)) and W satisfies some superquadratic condition different from the type of Ambrosetti-Rabinowitz.

We study this problem by virtue of some weak linking theorem recently developed and prove the existence of homoclinic orbits.