摘要：
In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy-Sobolev equation with critical growth: {-Delta u=vertical bar u vertical bar(2)*((t)-2)u/vertical bar y vertical bar(t) + mu u, in Omega u=0, on partial derivative Omega provided N > 6 + t, where 2*(t) = 2(N-t)/N-2, 0 <= t < 2, x = (y, z) is an element of R-k x RN-k, 2 <= k < N, mu > 0 and Omega is an open bounded domain in R-N, which contains some points x(0) (0, z(0)). Copyright (C) 2013 John Wiley & Sons, Ltd.
作者机构：
[Cao, Daomin] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.;[Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Shusen] Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia.
通讯机构：
[Peng, Shuangjie] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Asymptotic behaviour;Ground state solutions;Hénon equation
作者机构：
[Kang, Dongsheng] S Cent Univ Natl, Dept Math, Wuhan 430074, Peoples R China.;[Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430071, Peoples R China.
摘要：
Let N >= 3, lambda > 0, beta <= 0, N + beta - 2 > 0, N + alpha > 0, N + sigma > 0, alpha + 2 > beta, sigma + 2 > beta, beta/2 >= sigma/p(beta,sigma), 1 < q < min(p(beta, sigma)), p(s, t) := 2(N+t)/N+s-2 be the critical Sobolev-Hardy exponent. Via the variational methods, we prove the existence of a nontrivial solution to the singular semilinear problem -div (vertical bar x vertical bar(beta)del u) = vertical bar x vertical bar(alpha) vertical bar u vertical bar(p(beta,alpha)-2)u + lambda a(x)vertical bar u vertical bar(q-2)u, u >= 0 in R-N for suitable parameters N, lambda, q and some kinds of functions a (x). (c) 2007 Elsevier Ltd. All rights reserved.
