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Homoclinic orbits for a class of Hamiltonian systems. (English) Zbl 0705.34054
The author proves, under certain conditions, the existence of homoclinic orbits emanating from 0 for the second order Hamiltonian systems $(*)\quad \ddot q+V\sb q(t,q)=0,$ where $q\in R\sp n$ and $V\in C\sp 1(R\times R\sp n,R)$ is T-periodic in t. The homoclinic solution q of (*) has been found as the limit, as $k\to \infty$, of 2kT periodic solutions $q\sb k$. The approximating solutions $q\sb k$ are, in turn, obtained via the Mountain Pass Theorem.
Reviewer: N.Parhi

34C37Homoclinic and heteroclinic solutions of ODE
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE
70H05Hamilton’s equations
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