Multiple solutions for p-Laplacian systems with critical homogeneous nonlinearity
School of Mathematics and Statistics, Hubei Engineering University, Hubei 432000, P. R. China
Boundary Value Problems 2012, 2012:27 doi:10.1186/1687-2770-2012-27Published: 28 February 2012
In this article, we deal with existence and multiplicity of solutions to the p-Laplacian system of the type
where Ω ⊂ ℝN is a bounded domain with smooth boundary ∂Ω, Δpu = div(|∇u|p-2∇u) is the p-Laplacian operator, denotes the Sobolev critical exponent, is a homogeneous function of degree p*. By using the variational method and Ljusternik-Schnirelmann theory, we prove that the system has at least catΩ(Ω) distinct nonnegative solutions.
AMS 2010 Mathematics Subject Classifications: 35J50; 35B33.