Ground States for a Nonlinear Schrodinger System with Sublinear Coupling Terms

被引：8
|
作者：
Oliveira, Filipe [1 ]
Tavares, Hugo [2 ,3 ]
机构：
[1] Univ Nova Lisboa, Dept Math, FCT UNL, Caparica Campus, P-2829516 Lisbon, Portugal
[2] Univ Lisbon, IST, CAMGSD, Ave Rovisco Pais, P-1049001 Lisbon, Portugal
[3] Univ Lisbon, IST, Dept Math, Ave Rovisco Pais, P-1049001 Lisbon, Portugal
来源：
ADVANCED NONLINEAR STUDIES | 2016年 / 16卷 / 02期
基金：
欧洲研究理事会;
关键词：
Nontrivial Ground States; Coupled Nonlinear Schrodinger Systems; Nehari Manifold; SOLITARY WAVES; POSITIVE SOLUTIONS; EXISTENCE; EQUATIONS;
D O I：
10.1515/ans-2015-5029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the existence of ground states for the coupled Schrodinger system {-Delta u(i) + lambda(i)u(i) = mu(i)vertical bar ui vertical bar(2q-2) ui + Sigma(j not equal i) b(ij)vertical bar u(j)vertical bar(q)vertical bar u(i)vertical bar(q-2)u(i), {u(i) is an element of H-1 (R-n), i = 1,......, d, n >= 1, for lambda(i), mu(i) > 0, b(ij) = b(ji) > 0 (the so-called "symmetric attractive case") and 1 < q < n/(n - 2)(+). We prove the existence of a nonnegative ground state (u(1)*,......,u(d)*) with u(i)* radially decreasing. Moreover, we show that if in addition q < 2, such ground states are positive in all dimensions and for all values of the parameters.
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页码：381 / 387
页数：7
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