A necessary geometric condition for the existence of certain homoclinic orbits
Published online by Cambridge University Press: 24 October 2008
Extract
Throughout this brief note V denotes a fixed, smooth, real-valued function on such that there exists a bounded, open, strictly convex set C with
(the boundary of C), V > 0 in C, V = 0 on
and V′(0) = 0.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 591 - 594
- Copyright
- Copyright © Cambridge Philosophical Society 1986
References
REFERENCES
[1]Toland, J. F., The existence of symmetric homoclinic orbits for systems of Euler—Lagrange equations. Proc. A.M.S. Symposium (Berkeley), (1983), (to appear).Google Scholar
[2]Hofer, H., and Toland, J. F., Homoclinic, heteroclinic and periodic solutions for indefinite Hamiltonian systems. Math. Ann. 268 (1984), 387–403.CrossRefGoogle Scholar
[3]Toland, J. F., Hamiltonian systems with a natural order structure. Nonlinear functional analysis and its applications (Reidel, 1986), 147–160.CrossRefGoogle Scholar
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