Existence and multiplicity of positive solutions for Neumann problems involving singularity and critical growth

In this paper, the existence and multiplicity of positive solutions is established for a class of Numann problems of the form {-Delta u = u(2-1) + lambda/u(r), in Omega partial derivative u/partial derivative v = 0, on partial derivative Omega, here Omega is a smooth bounded domain in R-N, N >= 3, 2* = 2N/N-2, gamma is an element of (0,1) and lambda > 0 is a real parameter, partial derivative/partial derivative v is the outer normal derivative. The main technical approach is based on the variational and perturbation methods. (C) 2017 Elsevier Inc. All rights reserved.