Nonlinear Wave Equations: Constraints on Periods and Exponential Bounds for Periodic Solutions.

We show there is an upper bound to the allowed frequencies of time periodic solutions of a class of nonlinear wave equations: if ' is a 2=! -periodic solution then (0), where f is the nonlinearity. We also prove that Z 2=! 2jxj j'(x; t)j + jr'(x; t)j x dt < 1 for all where bac denotes the integer part of a