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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 $\stackrel{˙}{z}=𝒥{H}_{z}\left(t,z\right),$ where the Hamiltonian function $H\left(t,z\right)$ is nonperiodic in $t\in ℝ$ and superquadratic in $z\in {ℝ}^{2N}$. 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 (nonlinear dynamics) 70G75 Variational methods for dynamical systems
##### Keywords:
critical point; mild conditions; variational methods