On two conjectures in the fixed membrane eigenvalue problem |
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| Authors: | Lawrence E Payne |
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| Institution: | 1. Dept. of Mathematics, Cornell University, Ithaca, N.Y., USA
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| Abstract: | In this paper we give conditions sufficient to insure that the following two results hold for eigenfunctions of the fixed membrane problem defined over a bounded region of the plane: - The first eigenfunction has only one interior critical point.
- The second eigenfunction has no closed interior nodal curve.
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