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.


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


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