Existence of Multiple Positive Solutions for Brezis-Nirenberg-Type Problems Involving Singular Nonlinearities

This article is devoted to the existence and multiplicity to the following Brezis-Nirenberg-type problems involving singular nonlinearities: {-Delta u(u = 0) = vertical bar u vertical bar(p- 1)u + lambda(vertical bar u vertical bar(-1-beta)/vertical bar x vertical bar(alpha))u in Omega (on z Omega), where Omega is a smooth bounded domain in R-N (N >= 3), 0 is an element of Omega, lambda > 0, p = 2* - 1 with 2* = 2N/(N - 2) is the critical Sobolev exponent, 0 <= alpha < N (p + beta)/(p + 1), and 0 < beta < 1. By using the Nehari manifold and maximum principle theorem, the existence of at least two distinct positive solutions is obtained.