Song You, Peihao Zhao, Qingxuan Wang
In this article, we study the coupled nonlinear Schrödinger equations with Choquard type nonlinearities
where ν1,ν2,μ1,μ2 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 ν1=ν2, 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
Beijing 100084, China
| Peihao Zhao |
School of Mathematics and Statistics
Lanzhou, Gansu 730000, China
| Qingxuan Wang |
Department of Mathematics
Zhejiang Normal University
Jinhua, Zhejiang 321004, China
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