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

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