Newton's method and periodic solutions of nonlinear wave equations
Authors:
- 1 December 1993
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 46 (11) , 1409-1498
Abstract
We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. 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. © 1993 John Wiley & Sons, Inc.Keywords
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