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, where ω is a bounded domain with smooth boundary in rⁿ, p,s≥0 and q,r>0. our results are obtained in a range of p,q,r,s different from those in [m. ghergu, lane–emden systems with negative exponents, j. funct. anal. 258 (2010) 3295–3318].