Solutions to critical elliptic equations with multi-singular inverse square potentials

Let Omega be an open-bounded domain in RN (N >= 3) with smooth boundary partial derivative Omega. We are concerned with the multi-singular critical elliptic problem [GRAPHICS] where mu(i) is an element of R, 2* = 2N/N-2, a(i) is an element of Omega (1 <= i <= k) and Q (x) is a positive bounded function on Omega. Using Moser iteration, we prove the asymptotic behavior of solutions for (*) at points a(i) (1 <= i <= k). By exploiting the effect of the coefficient of the critical nonlinearity, we, by means of a variational method, establish the existence of positive and sign-changing solutions for problem (*). (c) 2005 Elsevier Inc. All rights reserved.