Generic existence of nondegenerate homoclinic solutions
- Authors: Motreanu D.1, Motreanu V.V.2
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Affiliations:
- Université de Perpignan
- Collège Jean Moulin
- Issue: Vol 38, No 2 (2017)
- Pages: 322-329
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199037
- DOI: https://doi.org/10.1134/S1995080217020159
- ID: 199037
Cite item
Abstract
The paper focuses on the homoclinic solutions of a general second order Hamiltonian system. By applying an abstract parametric transversality result, it is shown that generically the problem admits finitely many homoclinic solutions. These solutions are nondegenerate in the sense that they correspond to nondegenerate critical points of the associated functional and depend smoothly on the vector field.
Keywords
About the authors
D. Motreanu
Université de Perpignan
Author for correspondence.
Email: motreanu@univ-perp.fr
France, Perpignan, 66860
V. V. Motreanu
Collège Jean Moulin
Email: motreanu@univ-perp.fr
France, Tomblaine, 54510