arXiv 1711.080692017-11-21math.DS

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

Bochao Chen, Yong Li, Yixian Gao

DOI：: 10.1002/mma.4758

英文摘要：

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 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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