Ground states for a nonhomogeneous elliptic system involving Hardy-Sobolev critical exponents

This paper studies the following nonhomogeneous elliptic system involving Hardy-Sobolev critical exponents {Delta u + lambda(1) u(p-1)/vertical bar x vertical bar(s) + mu(1) u(2)*((s1)-1)/vertical bar x vertical bar(s1) + alpha gamma/2*(s(2)) u(alpha-1)v(beta)/vertical bar x vertical bar(s2) = 0 in Omega, Delta v + lambda(2) v(p-1)/vertical bar x vertical bar(s) + mu(2) v(2)*((s1)-1)/vertical bar x vertical bar(s1) + beta gamma/2*(s(2)) u(alpha)v(beta-1)/vertical bar x vertical bar(s2) = 0 in Omega, u >= 0, v >= 0 in Omega, u = 0, v = 0 on partial derivative Omega, where lambda(1), lambda(2), mu(1), mu(2), gamma > 0, 2 < p < 2*(s) := 2(N-s)/N-2, 0 <= s < 2, 0 < s(1), s(2) < 2, alpha, beta > 1, alpha + beta = 2*(s(2)), Omega is a C-1 open bounded domain in R-N containing the origin, and N >= 4. The existence result of positive ground state solution is established. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim