96-155 R.M. Pyke, I.M.Sigal

Nonlinear Wave Equations: Constraints on Periods and Exponential Bounds for Periodic Solutions (126K, LaTeX) Apr 26, 96

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Abstract. We show there is an upper bound to the allowed frequencies of time periodic solutions of a class of nonlinear wave equations: if phi is a 2pi/omega -periodic solution then (omega)^2 is less than or equal to f'(0) where f is the nonlinearity. We also prove that int_{0}^{2pi/omega}int_{RRn} exp^{2a|x|}(phi)^2 dxdt is finite for all a^2 less than f'(0) - [sqrt{f'(0)/omega^2}] where [c] denotes the integer part of c.

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