On a nonlinear elliptic eigenvalue problem

Let N(λ) be the number of the solutions of the equation: − u = λf (u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in RN (N 2) with smooth boundary. Under suitable conditions on f, we proved that N(λ)→+∞as λ→+∞.  2005 Elsevier Inc. All rights reserved