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| DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION |
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Citation： |
SHI Yuming.DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION[J].Chinese Annals of Mathematics B,2000,21(3):297~322 |
| Page view： 1056
Net amount： 740 |
Authors： |
SHI Yuming; |
Foundation： |
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-Franc,ais de Mathematiques Appliquees (ISFMA). |
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| 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. |
Keywords： |
Klein-Gordon equation, Periodic solution, Newton iteration |
Classification： |
35B10, 35L70 |
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