INFINITELY MANY POSITIVE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR FRACTIONAL SCALAR FIELD EQUATIONS

被引：28

作者：

Long, Wei ^{[1
,2
]}

Peng, Shuangjie ^{[1
]}

Yang, Jing ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[2] Jiangxi Normal Univ, Coll Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 02期

关键词：

Fractional Laplacian; nonlinear scalar field equation; reduction method; BOUND-STATES; EXISTENCE; REGULARITY; WAVES;

D O I：

10.3934/dcds.2016.36.917

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following nonlinear fractional scalar field equation (-Delta)(s)u + u = K(vertical bar x vertical bar u(p), u > 0 in R-N, where K(vertical bar x vertical bar) is a positive radial function, N >= 2, 0 < s < 1, and 1 < p < N+2s/N-2s. Under various asymptotic assumptions on K(x) at infinity, we show that this problem has infinitely many non-radial positive solutions and signchanging solutions, whose energy can be made arbitrarily large.

引用

页码：917 / 939

页数：23

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