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arXiv · 1711.08069

The Existence of Periodic Solutions for Nonlinear Beam Equations on $\mathbb T^d$ by a Para-differential Method

Bochao Chen·Yong Li·Yixian Gao
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Abstract

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 non-resonant 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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Bochao Chen, Yong Li, Yixian Gao. 2017-11-21. The Existence of Periodic Solutions for Nonlinear Beam Equations on $\mathbb T^d$ by a Para-differential Method. https://doi.org/10.1002/mma.4758

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