Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity

被引：10

作者：

Wang, Xing ^{[1
]}

Zhang, Li ^{[2
]}

机构：

[1] Xian Univ Technol, Sch Sci, Xian 710054, Shaanxi, Peoples R China

[2] Changan Univ, Sch Sci, Xian 710064, Shaanxi, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2019年 / 74卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fractional Laplacian; nondifferentiable functional; existence and multiple; REGULARITY; EQUATIONS; BOUNDARY; SOBOLEV;

D O I：

10.1007/s00025-019-1004-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of a class of fractional Laplacian with a singular nonlinearity. The purpose of this article is to give the existence and multiplicity of weak positive solutions by the combined effects of a superlinear and singular term. It is worth pointing out that the testing function in the definition of weak positive solutions does not need to have compact support in bounded domain. Hence the results of this paper are new even in the fractional Laplacian case.

引用

页数：18

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