Nonlinear wave equations: constraints on periods and exponential bounds for periodic solutions
Randall Pyke, Israel Michael Sigal · Duke Mathematical Journal · 1997
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.