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

共 50 条

[31] Existence and multiplicity of solutions for perturbed fractional p-Laplacian equations with critical nonlinearity in RN
Li, Qin
Yang, Zuodong
APPLICABLE ANALYSIS, 2023, 102 (11) : 2960 - 2977
[32] Existence, nonexistence, and multiplicity of solutions for the fractional -Laplacian equation in
Chen, Caisheng
Bao, Jinfeng
BOUNDARY VALUE PROBLEMS, 2016,
[33] Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms
Amiri, Shahla
Nyamoradi, Nemat
Behzadi, Abolfazl
Ambrosio, Vincenzo
POSITIVITY, 2021, 25 (04) : 1373 - 1402
[34] Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms
Shahla Amiri
Nemat Nyamoradi
Abolfazl Behzadi
Vincenzo Ambrosio
Positivity, 2021, 25 : 1373 - 1402
[35] Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity
Shen, Zifei
Gao, Fashun
ABSTRACT AND APPLIED ANALYSIS, 2013,
[36] BIFURCATION AND MULTIPLICITY OF SOLUTIONS FOR THE FRACTIONAL LAPLACIAN WITH CRITICAL EXPONENTIAL NONLINEARITY
Mishra, Pawan Kumar
Sreenadh, Konijeti
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
[37] Existence and Multiplicity of Positive Solutions for a Class of m-Point Fractional Differential Equations with p-Laplacian Operators
Xu, Baiyan
Yang, Yang
2020 3RD INTERNATIONAL CONFERENCE ON COMPUTER INFORMATION SCIENCE AND APPLICATION TECHNOLOGY (CISAT) 2020, 2020, 1634
[38] Existence of positive solutions to a class of p(x)-Laplacian equations with singular nonlinearities
Zhang, Qihu
APPLIED MATHEMATICS LETTERS, 2012, 25 (12) : 2381 - 2384
[39] Existence of positive solutions for a parameter fractional p-Laplacian problem with semipositone nonlinearity
Lopera, Emer
Lopez, Camila
Vidal, Raul E.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 526 (02)
[40] Positive solutions to a fractional equation with singular nonlinearity
Adimurthi
Giacomoni, Jacques
Santra, Sanjiban
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (04) : 1191 - 1226

← 1 2 3 4 5 →