Nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity

We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem−Δu=a(x)uq+λb(x)upin Ω,u=0on ∂Ω, where Ω   is a bounded domain in RNRN, λ∈Rλ∈R, 0