English

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

Dynamical Systems 2018-05-09 v1

Abstract

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the dd-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.

Keywords

Cite

@article{arxiv.1711.08069,
  title  = {The Existence of Periodic Solutions for Nonlinear Beam Equations on $\mathbb T^d$ by a Para-differential Method},
  author = {Bochao Chen and Yong Li and Yixian Gao},
  journal= {arXiv preprint arXiv:1711.08069},
  year   = {2018}
}