Nontrivial solutions for nonlinear Schrodinger-Choquard equations with critical exponents

被引：7
|
作者：
Luo, Huxiao [1 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2020年 / 107卷
基金：
中国国家自然科学基金;
关键词：
Variational methods; Nonlinear Schrodinger-Choquard equations; Lower and upper critical exponents; Hardy-Littlewood-Sobolev inequality; EXISTENCE;
D O I：
10.1016/j.aml.2020.106422
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the nonlinear Schrodinger-Choquard equation -Delta u + u = (I-alpha*vertical bar u vertical bar(P)) vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(q-2)u, x epsilon R-N, where N epsilon N, 0 < alpha < N, I-alpha denotes Riesz potential. When p = N+alpha/N or p = N+alpha/N-2, we get nontrivial solutions under some restrictions on N, q and alpha respectively. N+alpha/N and N+alpha/N-2 are lower and upper critical exponents in the sense of the Hardy-Littlewood-Sobolev inequality. This article extends some results of related literatures. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：7
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