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摘要
This paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (P-epsilon) : -Delta u = K vertical bar u vertical bar(4/(n-2)+epsilon) u in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-n, n %26gt;= 3, K is a C-3 positive function and e is a positive real parameter. We show first that in dimension 3, for epsilon small, (P-epsilon) has no sign-changing solutions with low energy which blow up at two points. For n %26gt;= 4, we prove that there are no sign-changing solutions which blow up at two nearby points. We also show that (P-epsilon) has no bubble-tower sign-changing solutions.
- 出版日期2012-2
