Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity

被引：0

作者：

Echarghaoui, Rachid ^{[1
]}

Khouakhi, Moussa ^{[2
]}

Masmodi, Mohamed ^{[1
]}

机构：

[1] Ibn Tofail Univ, Fac Sci, Dept Math LAGA, BP 133, Kenitra, Morocco

[2] Sidi Mohamed Ben Abdellah, Fac Sci, Dept Math LAMA, 1796 Atlas, Fes, Morocco

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2024年 / 27卷 / 02期

关键词：

Spectral fractional Laplacian (primary); critical elliptic problem; Nehari manifold; singularity; positive solutions; EXTENSION PROBLEM;

D O I：

10.1007/s13540-024-00242-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following problem {(-Delta)(s)u=g(x)u2 & lowast;s-1+lambda u-gamma,in Omega,u>0,in Omega, u=0, on partial derivative Omega, where Omega subset of R-N (N>2s) is a smooth bounded domain, s is an element of(0,1),lambda is a positive constant, 0<gamma <1, 2 & lowast;s=2NN-2sand(-Delta)sis the spectral fractional Laplacian. Based upon the Nehari manifold and using variational method we relate the number ofpositive solutions to the global maximum of the coefficient of the critical nonlinearity g.

引用

页码：772 / 798

页数：27

共 50 条

[1] Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity
Rachid Echarghaoui
Moussa Khouakhi
Mohamed Masmodi
[J]. Fractional Calculus and Applied Analysis, 2024, 27 : 772 - 798
[2] Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity
Xing Wang
Li Zhang
[J]. Results in Mathematics, 2019, 74
[3] Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity
Wang, Xing
Zhang, Li
[J]. RESULTS IN MATHEMATICS, 2019, 74 (02)
[4] Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity
Shen, Zifei
Gao, Fashun
[J]. ABSTRACT AND APPLIED ANALYSIS, 2013,
[5] On multiplicity of positive solutions for N-Laplacian with singular and critical nonlinearity
Goyal, Sarika
Sreenadh, K.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2014, 59 (12) : 1636 - 1649
[6] MULTIPLICITY OF POSITIVE SOLUTIONS FOR FRACTIONAL LAPLACIAN EQUATIONS INVOLVING CRITICAL NONLINEARITY
Zhang, Jinguo
Liu, Xiaochun
Mao, Hongying
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 53 (01) : 151 - 182
[7] Existence and multiplicity of positive solutions for a class of critical fractional Laplacian systems
Rachid Echarghaoui
Moussa Khouakhi
Mohamed Masmodi
[J]. Journal of Elliptic and Parabolic Equations, 2022, 8 : 813 - 835
[8] Existence and multiplicity of solutions for fractional Schodinger equation involving a critical nonlinearity
Yun, Yongzhen
An, Tianqing
Ye, Guoju
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)
[9] Existence and multiplicity of positive solutions for a class of critical fractional Laplacian systems
Echarghaoui, Rachid
Khouakhi, Moussa
Masmodi, Mohamed
[J]. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2022, 8 (02) : 813 - 835
[10] Positive solutions of fractional elliptic equation with critical and singular nonlinearity
Giacomoni, Jacques
Mukherjee, Tuhina
Sreenadh, Konijeti
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2017, 6 (03) : 327 - 354

← 1 2 3 4 5 →