In this paper we deal with multiplicity of positive solutions to the p-Laplacian equation of the type -div( ∇u p-2∇u) = μuq-1 + up*-1, u ∈ W01,p (Ω), where Ω ⊂ ℝN is a bounded domain, N ≥ p2, 2 ≤ p ≤ q < p*, p* = Np/(N - p), and μ is a positive parameter. We prove that there exists μ* > 0 such that, for each μ ∈ (0, μ*), the equation has at least catΩ(Ω) positive solutions. © 2003 Elsevier Science (USA). All rights reserved.
Alves, C. O., & Ding, Y. H. (2003). Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity. Journal of Mathematical Analysis and Applications, 279(2), 508–521. https://doi.org/10.1016/S0022-247X(03)00026-X