Uniqueness of Multiple-spike Solutions via the Method of Moving Planes
نویسندگان
چکیده
We study the uniqueness of multiple-spike solutions for some singularly perturbed Neumann problem in a ball. We are able to completely classify all two-peaked solutions. We can also classify all threepeaked solutions except some degenerate situations. Our main idea is by using the method of moving planes to show that two-peaks must be located on a line with the origin and the three-peaks must lie a twodimensional hyperplane with the origin. Then we compute the degree of these solutions and show the uniqueness of such solutions.
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