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Emily M. Fischer

Thesis

Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear Laplace-Beltrami Equations on the Unit Sphere

Advisor
Alfonso Castro
Second Reader(s)
Weiqing Gu

Abstract

In this thesis, I show that the semilinear Laplace-Beltrami Equation 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.

Additional Materials

Poster