Note on ground states of a nonlinear Schrodinger system

被引:5
|
作者
Chang, Jinyong [1 ]
机构
[1] Changzhi Univ, Dept Math, Changzhi 046011, Shanxi, Peoples R China
关键词
Schrodinger system; Nontrivial ground state; Morse index; PARTIALLY COHERENT SOLITONS; BOUND-STATES; EQUATIONS; WAVES;
D O I
10.1016/j.jmaa.2011.02.043
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We give a sufficient condition for the existence of positive radial ground states of the time-independent Schrodinger system {-Delta u(1) + lambda u(1) = mu(1)u(1)(3) + beta(12)u(2)(2)u(1) + beta(13)u(3)(2)u(1), in R-n, -Delta u(2) + lambda u(2) = beta(12)u(1)(2)u(2) + mu(2)u(2)(3) + beta(23)u(3)(2)u(2), in R-n, -Delta u(3) + lambda u(3) = beta(13)u(1)(2)u(3) + beta(23)u(2)(2)u(3) + mu(3)u(3)(3), in R-n, u(1)(x) -> 0, u(2)(x) -> 0, u(3)(x) -> 0, as |x| -> infinity, where n = 1,2,3, lambda > 0, mu j > 0 and beta ij > 0 (i < j) for i, j = 1,2,3. And in some special cases, our conditions are also necessary. (C) 2011 Elsevier Inc. All rights reserved.
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页码:957 / 962
页数:6
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