Multiple solutions for some elliptic equations with a nonlinearity concave at the origin

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem −Δu=−λ|u|q−2u+au+g(u)in Ωu=0on ∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain with smooth boundary ∂Ω∂Ω, g:R→Rg:R→R is a function of class C1C1 such that g(0)=g′(0)=0g(0)=g′(0)=0, λ>0λ>0 is a real parameter, a∈Ra∈R, and 1