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DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION
https://doi.org/10.1142/S0252959900000327Cited by:0 (Source: Crossref)
Abstract
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.
Project supported by the Special Funds for Major State Basic Research Projects of China, the Laboratory of Mathematics for Nonlinear Sciences, Fudan university, and the Institut Sino-Francais de Mathématiques Appliquées (ISFMA).
Document code: A, Article ID 0252-9599(2000)03-0297-26.
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