科研之友
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摘要
In this paper we consider the problem %26lt;br%26gt;-Delta u = up in Omega(R), %26lt;br%26gt;u = 0 on partial derivative Omega(R), %26lt;br%26gt;where p %26gt; 1 and Omega(R) is a smooth bounded domain with a hole which is diffeomorphic to an annulus and expands as R -%26gt; infinity. The main goal of the paper is to prove, for large R, the existence of a positive solution to (0.1) which is close to the positive radial solution in the corresponding diffeomorphic annulus. The proof relies on a careful analysis of the spectrum of the linearized operator at the radial solution as well as on a delicate analysis of the nondegeneracy of suitable approximating solutions.
- 出版日期2012-2
