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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 (*)q ¨+V q (t,q)=0, where qR n and VC 1 (R×R n ,R) is T-periodic in t. The homoclinic solution q of (*) has been found as the limit, as k, of 2kT periodic solutions q k . The approximating solutions q k are, in turn, obtained via the Mountain Pass Theorem.
Reviewer: N.Parhi

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