Existence of standing waves for quasi-linear Schrödinger equations on Tn

Abstract

This paper is devoted to the study of the existence of standing waves for a class of quasi-linear Schrödinger equations on Tn with dimension n ≥ 3. By construction of a suitable Nash-Moser-type iteration scheme, we overcome the clusters of “small divisor” problem, then the existence of standing waves for quasi-linear Schrödinger equations is established.

Keywords

• schrödinger equation
• small divisors
• periodic solution
• 35j60
• 35r03
• 35b10