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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 $\dot z = \cal J H_z(t, z),$ where the Hamiltonian function $H(t,z)$ is nonperiodic in $t \in \Bbb R$ and superquadratic in $z \in \Bbb R^{2N}$. With certain mild conditions, we obtain the solutions via variational methods for strongly indefinite problems.

70H05Hamilton’s equations
70K44Homoclinic and heteroclinic trajectories (nonlinear dynamics)
70G75Variational methods for dynamical systems
Full Text: DOI
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