Existence and multiplicity of solutions for fractional Choquard equations

被引：49

作者：

Ma, Pei ^{[1
]}

Zhang, Jihui ^{[2
]}

机构：

[1] Nanjing Forestry Univ, Coll Sci, Nanjing 210037, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 164卷

关键词：

Critical nonlinearity; Ground state solutions; Fractional Choquard equation; Variational method; Lusternik-Schnirelmann category; theory; POSITIVE SOLUTIONS; SCHRODINGER-EQUATION;

D O I：

10.1016/j.na.2017.07.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following fractional order Choquard equation (-Delta)(alpha/2) u(x) + (lambda V(x) - beta)u - (|x|(-mu) * |u|(2)(mu)*)|u|(2)(mu)*(-2) u, x is an element of R-n , with the nonlinearity in the critical growth, where alpha is an element of (0, 2), n >= 3, lambda, beta is an element of R+ and 2*(mu) = (2n - mu)/(n - alpha). Using the variational method, we establish the existence and multiplicity of weak solutions. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：100 / 117

页数：18

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