Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent
Date
2023-01-26
Authors
Daoues, Adel
Hammami, Amani
Saoudi, Kamel
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study a nonlocal equation involving singular and critical Hardy-Sobolev non-linearities,
(-Δp)su - μ|u|p-2u/|x|sp = λu-α + |u|p*s(t)-2u/|x|t, in Ω,
u > 0, in Ω,
u = 0, in ℝN \ Ω,
where Ω ⊂ ℝN is a bounded domain with Lipschitz boundary and (-Δp)s is the fractional p-Laplacian operator. We combine some variational techniques with a perturbation method to show the existence of multiple solutions.
Description
Keywords
Nonlocal elliptic problem, Singular non-linearity, Variational method, Sobolev and Hardy non-linearities, Perturbation method, Multiple positive solutions
Citation
Daoues, A., Hammami, A., & Saoudi, K. (2023). Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent. <i>Electronic Journal of Differential Equations, 2023</i>(10), pp. 1-19.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.