Periodic Solutions of Perturbed Conservative Systems

James R. Ward
1978 Proceedings of the American Mathematical Society  
The existence of 27r-periodic solutions to the system x" + grad G(x) = p(t, x), p being 2w-periodic in /, is established under conditions at infinity on the Hessian matrix of G. The condition used is weaker than earlier known conditions of a similar nature. A MS (MOS) subject classifications (1970). Primary 34C25, 47H15; Secondary 34B15. Key words and phrases. Periodic solutions, boundary value problems, nonlinear system of ordinary differential equations, Hubert space methods.
doi:10.2307/2042791 fatcat:ghqlfmeaorctxkapgpl3xoojfy