Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent

[摘要] In this article we study a nonlocal equation involving singular and criticalHardy-Sobolev non-linearities, \[ \displaylines{(-\Delta_p)^su-\mu \frac{|u|^{p-2}u}{|x|^{sp}}=\lambda u^{-\alpha}+\frac{|u|^{p_s^*(t)-2}u}{|x|^t}, \quad\text{in }\Omega,\\u>0,\quad\text{in }\Omega,\\u=0,\quad\text{in }\mathbb{R}^N\setminus\Omega, }\]where\(\Omega \subset \mathbb{R}^N\)is a bounded domain with Lipschitz boundary and\( (-\Delta_p)^s\)is the fractional p-Laplacian operator. We combine some variational techniques with a perturbation method to show the existence of multiple solutions.

[学科分类] 数学（综合）

[关键词] Nonlocal elliptic problem;singular non-linearity;variational method;Sobolev and Hardy non-linearities;perturbation method;multiple positive solutions