Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations

Meina Gao

doi:10.3934/dcds.2015.35.173

Article Contents

2015, Volume 35, Issue 1: 173-204. Doi: 10.3934/dcds.2015.35.173

This issue Previous Article Liouville theorem for an integral system on the upper half space Next Article Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case

Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations

Meina Gao^1,

1.
School of Science, Shanghai Second Polytechnic University, Shanghai 201209

Received: January 2014

Revised: April 2014

Published: January 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we establish an estimate for the solutions of a small-divisor equation with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the derivative nonlinear Schrödinger equations subject to small Hamiltonian perturbations.

Keywords:

KAM theory,
derivative nonlinear Schrödinger equation,
multiple normal frequencise.

Mathematics Subject Classification: Primary: 37K55; Secondary: 35Q55.

Citation:

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