Electron. J. Differential Equations, Vol. 2021 (2021), No. 47, pp. 1-20.

Existence and asymptotic behavior of positive least energy solutions for coupled nonlinear Choquard equations

Song You, Peihao Zhao, Qingxuan Wang

In this article, we study the coupled nonlinear Schrödinger equations with Choquard type nonlinearities

where ν1212 are positive constants, β>0 is a coupling constant, N≥3, α in (0,N) ∩ (0,4), and "*'" is the convolution operator. We show that the nonlocal elliptic system has a positive least energy solution for positive small β and positive large β via variational methods. For the case in which ν12, μ1≄μ2, N=3,4,5 and α=N-2, we prove the uniqueness of positive least energy solutions. Moreover, the asymptotic behaviors of the positive least energy solutions as β→ 0+ are studied.

Submitted July 17, 2019. Published May 28, 2021.
Math Subject Classifications: 35B40, 35J47, 35J50.
Key Words: Coupled Choquard equations; positive least energy solution; asymptotic behavior; variational method.

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  Song You
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China
email: yousong@mail.tsinghua.edu.cn
Peihao Zhao
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: zhaoph@lzu.edu.cn
  Qingxuan Wang
Department of Mathematics
Zhejiang Normal University
Jinhua, Zhejiang 321004, China
email: wangqx@zjnu.edu.cn

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