On a nonhomogeneous elliptic system with changing sign data

In this paper, we give some existence results for multiple positive solutions to the following nonhomogeneous elliptic system: (Sλ,μ){−Δu=au+(α+1)u|u|α−1|v|β+1+λf(x)in Ω−Δv=bv+(β+1)|u|α+1v|v|β−1+μg(x)in Ωu=v=0on ∂Ω, where ΩΩ is a regular bounded domain in RNRN(N≥3)(N≥3); α,β>0α,β>0; a,ba,b nonnegative reals; λλ and μμ are positive parameters and ff, gg are given changing sign functions.