We prove the existence of periodic solutions of the nonlinear wave equationsatisfying either Dirichlet or periodic boundary conditions on the interval 10, rr]. 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.