## 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

### Keywords:

critical point; mild conditions; variational methods
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### References:

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