摘要 : We consider the problem -Delta u = vertical bar u vertical bar(2)*(-2)u in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-N, N >= 3, and 2* = 2N/N-2 is the critical Sobolev exponent. We assum... 展开 We consider the problem -Delta u = vertical bar u vertical bar(2)*(-2)u in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-N, N >= 3, and 2* = 2N/N-2 is the critical Sobolev exponent. We assume that. is annular shaped, i.e. there are constants R-2 > R-1 > 0 such that {x epsilon R-N : R-1 < vertical bar x vertical bar < R-2} subset of Omega and {x epsilon R-N : vertical bar x vertical bar < R-1}\Omega not equal circle divide. Coron [7] showed that there is one positive solution to this problem if R-2/R-1 is large enough. We establish the existence of at least two pairs of nontrivial solutions in this case. The proof combines a deformation argument on the Nehari manifold with cohomological information derived from Dold's fixed point transfer. To deal with the lack of compactness, an energy estimate recently proved by one of the authors is used. 收起