Existence of nontrivial solutions for fractional Schrodinger equations with critical or supercritical growth

被引：10

作者：

Li, Quanqing ^{[1
]}

Teng, Kaimin ^{[2
]}

Wu, Xian ^{[3
]}

Wang, Wenbo ^{[4
]}

机构：

[1] Honghe Univ, Dept Math, Mengzi, Peoples R China

[2] Taiyuan Univ Technol, Dept Math, Taiyuan, Shanxi, Peoples R China

[3] Yunnan Normal Univ, Dept Math, Kunming, Yunnan, Peoples R China

[4] Yunnan Normal Univ, Dept Math & Stat, Kunming 650091, Yunnan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 05期

基金：

中国国家自然科学基金; 山西省青年科学基金;

关键词：

critical or supercritical growth; fractional Schrodinger equation; variational methods;

D O I：

10.1002/mma.5441

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following fractional Schrodinger equation with critical or supercritical growth (-Delta)su+V(x)u=f(x,u)+lambda|u|p-2u,x is an element of RN, where 0 < s < 1, N > 2s, lambda > 0, 2s*=2NN-2s, p >= 2s*, ( - Delta)(s) denotes the fractional Laplacian of order s and f is a continuous superlinear but subcritical function. Under some suitable conditions, we prove that the equation has a nontrivial solution for small lambda > 0 by variational methods. Our main contribution is related to the fact that we are able to deal with the case p>2s*.

引用

页码：1480 / 1487

页数：8

共 16 条

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