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Uniqueness of positive solutions to a Schrödinger system with linear and nonlinear couplings
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2021-07-16 , DOI: 10.1016/j.bulsci.2021.103029
Xinqiu Zhang 1 , Lishan Liu 1
Affiliation  

In this paper, we consider the uniqueness of nontrivial positive radial solutions to the following Schrödinger system with linear and nonlinear couplings:{u1+V1(x)u1=μ1u13+βu1u22+κu2inRN,u2+V2(x)u2=μ2u23+βu12u2+κu1inRN,u1(x),u2(x)>0inRN(N3),u1(x),u2(x)0 as|x|. By using the a priori estimate technique, we obtain interesting uniqueness results for two cases: (1) sufficiently small β,κ>0, (2) large β>0.



中文翻译:

具有线性和非线性耦合的薛定谔系统的正解的唯一性

在本文中,我们考虑以下具有线性和非线性耦合的薛定谔系统的非平凡正径向解的唯一性:{-1+1(X)1=μ113+β122+κ2电阻N,-2+2(X)2=μ223+β122+κ1电阻N,1(X),2(X)>0电阻N(N3),1(X),2(X)0 作为|X|. 通过使用先验估计技术,我们在两种情况下获得了有趣的唯一性结果:(1)足够小 β,κ>0, (2) 大 β>0.

更新日期:2021-07-22
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