Methods and Applications of Analysis

Volume 27 (2020)

Number 3

Infinitely many synchronized solutions to a nonlinearly coupled Schrödinger equations with non-symmetric potentials

Pages: 243 – 274



Chunhua Wang (School of Mathematics and Statistics, Central China Normal University, Wuhan, China)

Jing Zhou (School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China)


We study a nonlinearly coupled Schrödinger equations in $\mathbb{R}^N (2 \leq N \lt 6)$. Assume that the potentials in the system are continuous functions satisfying some suitable decay assumptions but without any symmetric properties, and the parameters in the system satisfy some restrictions. Applying the Liapunov–Schmidt reduction methods twice and combining localized energy method, we prove that the problem has infinitely many positive synchronized solutions.


nonlinear Schrödinger equations, non-symmetric potentials, synchronized solutions

2010 Mathematics Subject Classification

35B99, 35J10, 35J60

This work was partially supported by the NSFC with grant nos. 12071169 and CCNU18CXTD04.

Received 21 May 2020

Accepted 23 December 2020

Published 13 August 2021