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

✍ Scribed by Xue-Feng Yang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 417 KB
• Volume: 160
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3301

✦ 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