You, SongZhao, PeihaoWang, Qingxuan2021-08-262021-08-262021-05-28You, S., Zhao, P., & Wang, Q. (2021). Existence and asymptotic behavior of positive least energy solutions for coupled nonlinear Choquard equations. <i>Electronic Journal of Differential Equations, 2021</i>(47), pp. 1-20.1072-6691https://hdl.handle.net/10877/14457In this article, we study the coupled nonlinear Schrödinger equations with Choquard type nonlinearities -Δu + v1u = μ1 (1/|x|α ∗ u2)u + β(1/|x|α *v2u in ℝN, -Δv + v2v = μ2 (1/|x|α ∗ v2)v + β(1/|x|α ∗ u2 in ℝN, u, v ≥ 0 in ℝN, u, v ∈ H1(ℝN), where v1, v2, μ1, μ2 are positive constants, β > 0 is a coupling constant, N ≥ 3, α ∈ (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 v1 = v2, energy solutions. Moreover, the asymptotic behaviors of the positive least energy solutions as β → 0+ are studied.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalCoupled Choquard equationsPositive least energy solutionAsymptotic behaviorVariational methodArticle