# Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth

Volume 10, Issue 9, pp 4930--4939
Publication Date: September 22, 2017 Submission Date: June 06, 2017
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### Authors

Peiluan Li - School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China. Yuan Yuan - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s NL A1B 3X7, Canada. Yuanxian Hui - School of Mathematics and Statistics, Puer University, Puer 665000, China.

### Abstract

In this paper, we investigate the small energy solutions for a coupled fractional Schrödinger system with critical growth. The existence criteria of infinitely many small energy solutions are established without Ambrosetti-Rabinowitz (A-R) condition by variant fountain theorem. Our main results are completely new and complement the previously known studies.keywords

### Share and Cite

##### ISRP Style

Peiluan Li, Yuan Yuan, Yuanxian Hui, Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4930--4939

##### AMA Style

Li Peiluan, Yuan Yuan, Hui Yuanxian, Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth. J. Nonlinear Sci. Appl. (2017); 10(9):4930--4939

##### Chicago/Turabian Style

Li, Peiluan, Yuan, Yuan, Hui, Yuanxian. "Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4930--4939

### Keywords

• Coupled fractional Schr̈odinger system
• small energy solutions
• critical growth
• variant fountain theorem

•  26A33
•  34B37
•  34K10

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