GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

doi:10.1007/s10473-020-0105-0

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 59-74.doi: 10.1007/s10473-020-0105-0

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GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

Quanqing LI¹, Wenbo WANG², Kaimin TENG³, Xian WU⁴

1. Department of Mathematics, Honghe University, Mengzi 661100, China;
2. Department of Mathematics and Statistics, Yunnan University, Kunming 650091, China;
3. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;
4. Department of Mathematics, Yunman Normal University, Kunming 650092, China

Received:2019-01-23 Revised:2019-09-02 Online:2020-02-25 Published:2020-04-14
Contact: Kaimin TENG E-mail:tengkaimin2013@163.com
Supported by:
This work is supported in part by the National Natural Science Foundation of China (11801153; 11501403; 11701322; 11561072) and the Honghe University Doctoral Research Programs (XJ17B11, XJ17B12, DCXL171027, 201810687010) and the Yunnan Province Applied Basic Research for Youths (2018FD085) and the Yunnan Province Local University (Part) Basic Research Joint Project (2017FH001-013) and the Natural Sciences Foundation of Yunnan Province (2016FB011) and the Yunnan Province Applied Basic Research for General Project (2019FB001) and Technology Innovation Team of University in Yunnan Province.

Abstract

Abstract: In this article, we study the following fractional Schrödinger equation with electromagnetic fields and critical growth
(-△)_A^su + V (x)u = |u|^{2_s^*-2}u + λf(x,|u|²)u, x ∈ R^N,
where (-△)_A^s is the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2_s^* = 2N/(N-2s), f is a continuous function, V ∈ C(R^N, R) and A ∈ C(R^N, R^N) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.

Key words: fractional Schrödinger equation, fractional magnetic operator, critical growth

CLC Number:

35J20

Quanqing LI, Wenbo WANG, Kaimin TENG, Xian WU. GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH[J].Acta mathematica scientia,Series B, 2020, 40(1): 59-74.

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GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

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