Existence and asymptotic behavior of positive least energy solutions for coupled nonlinear Choquard equations
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Date
2021-05-28
Authors
You, Song
Zhao, Peihao
Wang, Qingxuan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Coupled Choquard equations, Positive least energy solution, Asymptotic behavior, Variational method
Citation
You, 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.
Rights
Attribution 4.0 International