Uniqueness of multiple-spike solutions via the method of moving planes
Resource
Pure and Applied Mathematics Quarterly 3 (3): 689-735
Journal
Pure and Applied Mathematics Quarterly
Pages
689-735
Date Issued
2007
Date
2007
Author(s)
Abstract
We study the uniqueness of multiple-spike solutions for some singularly perturbed Neumann problems in a ball. We completely classify all two-peaked solutions and, except in some degenerate situations, also all three-peaked solutions. Our main idea is using the method of moving planes to show that in the case of two peaks both of them must be located on a line containing the origin and for three peaks all of them must lie in a two-dimensional hyperplane containing the origin. Then we compute the degree of these solutions (restricted in certain symmetry class) and show their uniqueness.
Type
journal article
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