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

Electronic Journal of Differential Equations

article

Song You¹  Peihao Zhao²  Qingxuan Wang³ 

[1] Department of Mathematical Sciences Tsinghua University Beijing 100084;School of Mathematics and Statistics Lanzhou University Lanzhou;Department of Mathematics Zhejiang Normal University Jinhua

关键词: Coupled Choquard equations;    positive least energy solution;    asymptotic behavior;    variational method.;   

DOI  :  10.58997/ejde.2021.47

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article, we study the coupled nonlinear Schrödinger equations withChoquard type nonlinearitieswhere ν1,ν2,μ1,μ20 is a coupling constant, N≥3, α in (0,N) ∩ (0,4), and "*'" is the convolution operator.We show that the nonlocal elliptic systemhas a positive least energy solution for positive small β and positive largeβ 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 asβ→ 0+ are studied.

【 授权许可】

CC BY