Existence of homoclinic orbits for Hamiltonian systems with superquadratic potentials (Q963140)

Summary: This paper concerns solutions for the Hamiltonian system: \(\dot z={\mathcal J}H_z(t,z)\). Here \(H(t,z)=(1/2)z\cdot Lz+ W(t,z)\), \(L\) is a \(2N\times 2N\) symmetric matrix, and \(W\in C^1(\mathbb R\times\mathbb R^{2N},\mathbb R)\). We consider the case that \(0\in\sigma_c(-({\mathcal J}(d/dt)+L))\) 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.