## 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 $$(*)\quad \ddot q+V_ q(t,q)=0,$$ where $$q\in R^ n$$ and $$V\in C^ 1(R\times R^ n,R)$$ is T-periodic in t. The homoclinic solution q of (*) has been found as the limit, as $$k\to \infty$$, of 2kT periodic solutions $$q_ k$$. The approximating solutions $$q_ k$$ are, in turn, obtained via the Mountain Pass Theorem.
Reviewer: N.Parhi

### MSC:

 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 70H05 Hamilton’s equations
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### References:

 [1] DOI: 10.1016/0022-1236(73)90051-7 · Zbl 0273.49063 [2] Rabinowitz, Anal. Nonlineaire 6 pp 331– (1989) [3] Lions, Rev. Mat. Iberoamericana 1 pp 145– (1985) · Zbl 0704.49005 [4] DOI: 10.1002/cpa.3160310203
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