Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System

We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions...

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Bibliographic Details
Published in:	Acta mathematica scientia Vol. 40; no. 5; pp. 1585 - 1601
Main Authors:	Duan, Xueliang, Wei, Gongming, Yang, Haitao
Format:	Journal Article
Language:	English
Published:	Singapore Springer Singapore 01-09-2020 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China%College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Subjects:	Analysis Mathematics Mathematics and Statistics infinitely many solutions concentration compactness principle 35A15 coupled Schrödinger system ground state solution 35J60 coupled Schr(o)dinger system
Online Access:	Get full text
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Summary:	We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions for the system with close-to-periodic potentials.
ISSN:	0252-9602 1572-9087
DOI:	10.1007/s10473-020-0523-9