Positive solutions of Lane–Emden systems with negative exponents: Existence, boundary behavior and uniqueness

We study the existence, boundary behavior and uniqueness of solutions for the singular elliptic system −Δu=u−pv−q,−Δv=u−rv−s,u>0,v>0,x∈Ω,u|∂Ω=v|∂Ω=0−Δu=u−pv−q,−Δv=u−rv−s,u>0,v>0,x∈Ω,u|∂Ω=v|∂Ω=0, where ΩΩ is a bounded domain with smooth boundary in RNRN, p,s≥0p,s≥0 and q,r>0q,r>0. Our results are obtained in a range of p,q,r,sp,q,r,s different from those in [M. Ghergu, Lane–Emden systems with negative exponents, J. Funct. Anal. 258 (2010) 3295–3318].