Semilinear elliptic equations and nonlinearities with zeros

In this paper we consider the semilinear elliptic problem {−Δu=λf(u)in  Ω,u=0on  ∂Ω, where ff is a nonnegative, locally Lipschitz continuous function, ΩΩ is a smooth bounded domain and λ>0λ>0 is a parameter. Under the assumption that ff has an isolated positive zero αα such that f(t)(t−α)N+2N−2  is decreasing in  (α,α+δ), for some small δ>0δ>0, we show that for large enough λλ there exist at least two positive solutions uλ