DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION

By introducing the block estimate technique and directly using the Newton iteration method, the author constructs Cantor families of time periodic solutions to a class of nonlinear wave equations with periodic boundary conditions. The Lyapunov-Schmidt decomposition used by J. Bourgain, W. Craig and C. E. Wayne is avoided. Thus this work simplifies their framework for KAM theory for PDEs.