Multiple positive solutions for semilinear elliptic systems

This article investigates the effect of the coefficient f(z) of the critical nonlinearity. For sufficiently small λ, μ>0, there are at least k positive solutions of the semilinear elliptic systems{-δu=λg(z)|u|p-2u+αα+βf(z)|u|α-2u|v|βin Ω;-δv=μh(z)|v|p-2v+βα+βf(z)|u|α|v|β-2vin Ω;u=v=0on ∂Ω, where 0∈Ω⊂RN is a bounded domain, α>1, β>1 and 2<p<α+β=2 ^* for N>4.