I show that a class of semilinear Laplace-Beltrami equations has infinitely many solutions on the unit sphere which are symmetric with respect to rotations around some axis. This equation corresponds to a singular ordinary differential equation, which we solve using energy analysis. We obtain a Pohozaev-type identity to prove that the energy is continuously increasing with the initial condition and then use phase plane analysis to prove the existence of infinitely many solutions.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1057 |
| Date | 01 January 2014 |
| Creators | Fischer, Emily M |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
| Rights | © 2014 Emily Fischer |
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