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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on generalized solutions of singular Hamiltonian systems


Author: Kazunaga Tanaka
Journal: Proc. Amer. Math. Soc. 122 (1994), 275-284
MSC: Primary 58F05; Secondary 34C25, 58E05, 70H05
DOI: https://doi.org/10.1090/S0002-9939-1994-1204387-9
MathSciNet review: 1204387
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Abstract: We consider T-periodic solutions of singular Hamiltonian systems with weak force

$\displaystyle \ddot q + \nabla V(q,t) = 0,$

where $ V(q,t) \sim - 1/\vert q{\vert^\alpha }$ near $ q = 0$ with $ \alpha \in (0,2)$. In particular, we study some properties of generalized T-periodic solutions, which were introduced by Bahri and Rabinowitz.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1204387-9
Keywords: Periodic solutions, singular Hamiltonian systems, minimax methods
Article copyright: © Copyright 1994 American Mathematical Society