Abstract :
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∈W
1,p
0 (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
