Multiple positive solutions for semilinear elliptic systems

This article investigates the effect of the coefficient f(z)f(z) of the critical nonlinearity. For sufficiently small λ,μ>0λ,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⊂RN0∈Ω⊂RN is a bounded domain, α>1α>1, β>1β>1 and 24N>4.