Uniqueness and Eigenvalue Estimates of Boundary Spike Solutions
نویسنده
چکیده
We study the properties of single boundary spike solutions for the following singularly perturbed problem 2 u ? u + u p = 0 in ; u > 0 in and @u @ = 0 on @ It is known that at a nondegenerate critical point of the mean curvature function H (P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N ? 1) small eigenvalues. We obtain the exact asymptotics of the small eigenvalues in terms of H (P).
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تاریخ انتشار 1998