American Institute of Mathematical Sciences

January  2015, 35(1): 173-204. doi: 10.3934/dcds.2015.35.173

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

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

Received  January 2014 Revised  April 2014 Published  August 2014

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.
Citation: Meina Gao. Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 173-204. doi: 10.3934/dcds.2015.35.173
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