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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 z ˙=𝒥H z (t,z), where the Hamiltonian function H(t,z) is nonperiodic in t and superquadratic in z 2N . With certain mild conditions, we obtain the solutions via variational methods for strongly indefinite problems.
MSC:
70H05Hamilton’s equations
70K44Homoclinic and heteroclinic trajectories (nonlinear dynamics)
70G75Variational methods for dynamical systems
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