The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

被引：3
|
作者：
Chen, Bochao [1 ]
Li, Yong [1 ]
Gao, Yixian [1 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Ctr Math & Interdisciplinary Sci, Changchun 130024, Jilin, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 07期
关键词：
beam equations; iteration scheme; periodic solutions; para-differential conjugation; WAVE-EQUATIONS; SCHRODINGER-EQUATIONS; FORCED VIBRATIONS; KAM TORI; PERTURBATIONS;
D O I：
10.1002/mma.4758
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper focuses on the construction of periodic solutions of nonlinear beam equations on the d-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the nonresonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.
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页码：2546 / 2574
页数：29
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