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Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system. (English) Zbl 1162.70014

Summary: This paper deals with existence and exponential decay of homoclinic orbits for the first-order Hamiltonian system \(\dot z = \mathcal J H_z(t, z),\) where the Hamiltonian function \(H(t,z)\) is nonperiodic in \(t \in \mathbb R\) and superquadratic in \(z \in \mathbb R^{2N}\). With certain mild conditions, we obtain the solutions via variational methods for strongly indefinite problems.

MSC:

70H05 Hamilton’s equations
70K44 Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics
70G75 Variational methods for problems in mechanics
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