In this paper, we answer affirmatively an open problem (cf. Theorem 4 0 in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let O{0 be an open-bounded domain, OCR N ðNX5Þ and assume that 0pmoð NÀ2 2 Þ 2 À ð Nþ2 N Þ 2 ; then, for all l40 there exists a nontrivial solution with critical level in the range ð0; 1 N S N 2m Þ for the problem ÀDu À m u jxj 2 ¼ lu þ juj 2 Ã À2 u in O; u ¼ 0 on @O: r 2004 Elsevier Inc. All rights reserved.
Let be an open-bounded domain in R N (N 3) with smooth boundary * . We are concerned with the multi-singular critical elliptic problemwhere i ∈ R, 2 * = 2N N−2 , a i ∈ (1 i k) and Q(x) is a positive bounded function on . 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 ( * ).
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