Complete classification of ground state solutions with different Morse index for critical fractional Laplacian system

被引：1

作者：

Zhen, Maoding ^{[1
]}

Zhang, Binlin ^{[2
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Peoples R China

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 02期

基金：

中国国家自然科学基金;

关键词：

classification of solutions; fractional Laplacian system; ground state solution; morse index; variational method; LEAST ENERGY SOLUTIONS; CRITICAL EXPONENT; EXISTENCE; REGULARITY; EQUATIONS;

D O I：

10.1002/mma.6862

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first obtain the existence of positive ground state solutions for the following critical fractional Laplacian system {(-Delta)(s)u=mu(1)vertical bar u vertical bar(2s)*(-2)u+alpha gamma/2(s)*vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in Rn, (-Delta)(s)v=mu(2)vertical bar v vertical bar(2s)*(-2)v+beta gamma/2(s)*vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v in R-n, then we give a complete classification of positive ground state solutions with different Morse index. More precisely, we show that if (u, v) be any positive ground state solution of system (1.1), then (u, v) must be (C1U epsilon, y, C2U epsilon, y) type with Morse index 1 and Morse index 2, where U-epsilon,U- y is a positive ground state solution for a given equation.

引用

页码：1601 / 1614

页数：14

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