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Nodal Sets and Morse Indices of Solutions of Super-linear Elliptic PDEs

โœ Scribed by Xue-Feng Yang


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
417 KB
Volume
160
Category
Article
ISSN
0022-1236

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โœฆ Synopsis


In this paper, we develop a Sturm Liouville type theory for the nodal sets and Morse indices of solutions of super-linear elliptic PDEs with Dirichlet boundary condition. It shows that there are some relationships between analytic properties (e.g., L p -norm, vanishing order of the nodal point, and N&1 dimensional Hausdorff measure of the nodal set) of the solutions as the functions on the domain 0 and Morse indices of the solutions as the critical points of the functional


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