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Zbl 0705.34054
Rabinowitz, Paul H.
Homoclinic orbits for a class of Hamiltonian systems. (English)
[J] Proc. R. Soc. Edinb., Sect. A 114, No.1-2, 33-38 (1990). ISSN 0308-2105; ISSN 1473-7124/e

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.
[N.Parhi]

MSC 2000:: *34C37 Homoclinic and heteroclinic solutions of ODE
34C05 Qualitative theory of some special solutions of ODE
34C25 Periodic solutions of ODE
70H05 Hamilton's equations

Keywords: homoclinic orbits; second order Hamiltonian systems; Mountain Pass Theorem

Cited in: Zbl 1251.58003 Zbl 1190.34027 Zbl 0838.34058 Zbl 0836.34046

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