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.

引用

页码：2546 / 2574

页数：29

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