Multiplicity of positive solutions for a class of quasilinear nonhomogeneous Neumann problems

In this paper we study the existence, nonexistence and multiplicity of positive solutions for nonhomogeneous Neumann boundary value problem of the type { -Delta(p)u + lambdau(p-1) = u(q) in Omega, {u > 0 in Omega, {\delu\(p-2) partial derivativeu/partial derivativen=phi on partial derivativeOmega where Omega is a bounded domain in R-n with smooth boundary, 1 < p < n, Delta(P)u = div(\delu\(p-2)delu) is the p-Laplacian operator, p - 1 < q less than or equal to p* - 1, p* = np/(n - p), phi is an element of C-alpha (Omega), 0 < alpha < 1, phi not equivalent to 0, (x) greater than or equal to 0 and lambda is a real parameter. The proofs of our main results rely on different methods: lower and upper solutions and variational approach. (C) 2004 Elsevier Ltd. All rights reserved.