A note on generalized solutions of singular Hamiltonian systems

Abstract

We consider T-periodic solutions of singular Hamiltonian systems with weak force \[ q ¨ + ∇ V ( q , t ) = 0 , \ddot q + \nabla V(q,t) = 0, \] where V ( q , t ) ∼ − 1 / | q | α V(q,t) \sim - 1/|q{|^\alpha } near q = 0 q = 0 with α ∈ ( 0 , 2 ) \alpha \in (0,2) . In particular, we study some properties of generalized T-periodic solutions, which were introduced by Bahri and Rabinowitz.