92-1 Craig W., Wayne , C.E.
Newton's Method and Periodic Solutions of Nonlinear Wave Equations (238K, TeX) Jan 24, 92
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We prove the existence of periodic solutions of the nonlinear wave equation $$ \partial_t^2 u = \partial_x^2 u - g(x,u)~, $$ satisfying either Dirichlet or periodic boundary conditions on the interval $[0,\pi]$. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity $g(x,u)$ satisfies certain generic conditions of nonresonance and genuine nonlinearity.

Files: 92-1.tex