Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrodinger systems

被引:26
作者
Bartsch, Thomas [1 ]
Li, Houwang [2 ]
Zou, Wenming [2 ]
机构
[1] Univ Giessen, Math Inst, Arndtstr 2, D-35392 Giessen, Germany
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
关键词
STANDING WAVES; EQUATIONS; SYMMETRY;
D O I
10.1007/s00526-022-02355-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The paper is concerned with the existence and asymptotic properties of normalized ground states of the following nonlinear Schrodinger system with critical exponent: {-Delta u + lambda(1)u = vertical bar u vertical bar(2*-2)u + v alpha vertical bar u vertical bar(alpha-2)vertical bar v vertical bar(beta)u, in R-N, -Delta V + lambda(2)v = vertical bar v vertical bar(2*-2)v + v beta vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2) v, in R-N, integral(RN) u(2) =a(2), integral(RN) v(2) = b(2), where N = 3, 4, alpha, beta > 1, 2 < alpha + beta < 2* = 2N/N-2. We prove that a normalized ground state does not exist for. < 0. When. > 0 and alpha+ beta <= 2 + 4N, we show that the system has a normalized ground state solution for 0 < v < v(0), the constant v(0) will be explicitly given. In the case alpha + beta > 2 + 4/N we prove the existence of a threshold v(1) >= 0 such that a normalized ground state solution exists for v > v(1), and does not exist for v < v(1). We also give conditions for v(1) = 0. Finally we obtain the asymptotic behavior of the minimizers as v -> 0(+) or v ->+ infinity.
引用
收藏
页数:34
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