Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent
Texas State University, Department of Mathematics
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.
Nonlocal elliptic problem, Singular non-linearity, Variational method, Sobolev and Hardy non-linearities, Perturbation method, Multiple positive solutions
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.