A note on generalized solutions of singular Hamiltonian systems

Tanaka, Kazunaga

doi:10.1090/S0002-9939-1994-1204387-9

A note on generalized solutions of singular Hamiltonian systems
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Proc. Amer. Math. Soc. 122 (1994), 275-284 Request permission

Abstract:

We consider T-periodic solutions of singular Hamiltonian systems with weak force \[ \ddot q + \nabla V(q,t) = 0,\] where $V(q,t) \sim - 1/|q{|^\alpha }$ 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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