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October, 2017 Construction of Periodic Solutions for Nonlinear Wave Equations by a Para-differential Method
Bochao Chen, Yixian Gao, Yong Li
Taiwanese J. Math. 21(5): 1057-1097 (October, 2017). DOI: 10.11650/tjm/7914


This paper is concerned with the existence of families of time-periodic solutions for the nonlinear wave equations with Hamiltonian perturbations on one-dimensional tori. We obtain the result by a new method: a para-differential conjugation together with a classical iteration scheme, which have been used for the nonlinear Schrödinger equation in [22]. Avoiding the use of KAM theorem and Nash-Moser iteration method, though a para-differential conjugation, an equivalent form of the investigated nonlinear wave equations can be obtained, while the frequencies are fixed in a Cantor-like set whose complement has small measure. Applying the non-resonant conditions on each finite-dimensional subspaces, solutions can be constructed to the block diagonal equation on the finite subspace by a classical iteration scheme.


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Bochao Chen. Yixian Gao. Yong Li. "Construction of Periodic Solutions for Nonlinear Wave Equations by a Para-differential Method." Taiwanese J. Math. 21 (5) 1057 - 1097, October, 2017.


Received: 31 October 2016; Revised: 14 December 2016; Accepted: 15 December 2016; Published: October, 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06871359
MathSciNet: MR3707884
Digital Object Identifier: 10.11650/tjm/7914

Primary: 35L05, 35S50

Rights: Copyright © 2017 The Mathematical Society of the Republic of China


Vol.21 • No. 5 • October, 2017
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