A multiplicity results for a singular quasilinear elliptic equation.

The purpose of this work is to study the following singular problem: ( P λ) − div (a (x , ∇ u)) = u − α + λ u q in Ω ; u > 0 , in Ω ; u = 0 , in ℝ n ∖ Ω ; where Ω ⊂ ℝ N , N ≥ 2 be a bounded smooth domain, λ is a positive parameter, p ≥ 2 such that N ≥ p and 0 < α ≤ 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 , α such that for all λ ∈ (0 , T q , α) , problem (P λ) has at least two solutions. [ABSTRACT FROM AUTHOR]