Abstract
The purpose of this work is to study the following singular problem:
(P-lambda) {-div(a(x, del u)) = u(-alpha) + lambda u(q) in Omega; u > 0, in Omega; u = 0, in R-n\Omega;
where Omega subset of R-N, N >= 2 be a bounded smooth domain, lambda is a positive parameter, p >= 2 such that N >= p and 0 < alpha <= 1, p - 1 < q <= p* - 1, where p* = N-p/N-p. We employ the Nehari manifold approach and the fibering maps in order to show the existence of T-q,T-alpha such that for all lambda is an element of (0, T-q,T-alpha), problem (P-lambda) has at least two solutions.