科研之友
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摘要
We show that the critical problem
-Delta u = vertical bar u vertical bar(4/(N-2))u in Omega, u = 0 on partial derivative Omega,
has at least
max{cat(Theta, Theta \ BrM), cupl(Theta, Theta \ BrM) + 1} >= 2
pairs of nontrivial solutions in every domain Omega obtained by deleting from a given bounded smooth domain Theta subset of R-N a thin enough tubular neighborhood BrM of a closed smooth submanifold M of Theta of dimension <= N - 2, where "cat" is the Lusternik-Schnirelmann category and "cupl" is the cup-length of the pair.
- 出版日期2015-12
