Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity

For an open, bounded set Ω⊂RNΩ⊂RN with smooth boundary ∂Ω∂Ω, N≥3N≥3, γ>0γ>0, and 10Λ>0 such that the singular b.v.p.{−Δu=λuγ+up,x∈Ω,u=0,x∈∂Ω,has two positive solutions for every λ∈(0,Λ)λ∈(0,Λ). Given f∈Lm(Ω)f∈Lm(Ω) with m>1m>1 and MM a bounded elliptic matrix, we also study the Dirichlet b.v.p. associated to the related singular equation −div(M(x)∇z)=f(x)zγ,x∈Ω.