Subharmonic solutions of nonlinear wave equations onS n

In this paper we study a nonlinear wave equation on Sⁿ with a nonlinear term 2-periodic in t. More precisely we give a Birkoff-Lewis type result of existence of periodic solutions localized near an equilibrium point, that is we search for distinct 2k-periodic solutions (subharmonics) of the wave equation, k, which have small amplitude and minimal period 2k.Work supported by M.U.R.S.T. (Research funds 40% and 60%).