On a nonlinear elliptic eigenvalue problem

Let N(λ) be the number of the solutions of the equation: −Δu=λf(u)inΩ,u=0on∂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→+∞.