Existence and local uniqueness of multi-peak solutions for the Chern-Simons-Schrödinger system

被引:0
作者
Hua, Qiaoqiao [1 ]
Wang, Chunhua [2 ]
Yang, Jing [3 ]
机构
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan, Peoples R China
[3] Zhejiang Univ Technol, Dept Math, Zhenjiang 310014, Peoples R China
关键词
Multi-peak positive solutions; the finite-dimensional reduction method; local uniqueness; Pohozaev identities; NONLINEAR SCHRODINGER-EQUATIONS; BOUND-STATES; STANDING WAVES; BUMP;
D O I
10.1007/s11784-024-01131-w
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the Chern-Simons-Schrodinger system {- epsilon(2) Delta u +V(x)u + (A(0) + A(1)(2) +A(2)(2))u= | u |(p - 2) u, x is an element of R-2 , partial derivative(1) A(0) = A(2) u(2) , partial derivative(2) A(0) = -A(1)u(2), partial derivative(1) A(2) - partial derivative(2) A(1) = - 1/2 |u|(2), partial derivative(1) A(1) + partial derivative(2) A(2) = 0, where p > 2, , epsilon > 0 is a parameter and V : R-2 -> R is a bounded continuous function. Under some mild assumptions on V (x), exploiting the finite-dimensional reduction method, we construct multi-peak solutions of the problem above. Also, we prove that all the concentrated solutions of the problem have the same form. Meanwhile, we present that the concentrated solutions are locally unique by various local Pohozaev identities, blow-up analysis and the maximum principle. Because of the nonlocal terms involved by A(0) , A(1) and A(2) , we have to build a series of new and technical estimates which are very useful to study this problem.
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页数:41
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