Open Access Senior Thesis
Bachelor of Science
© 2014 Emily Fischer
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.
Fischer, Emily M., "Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear Laplace-Beltrami Equations on the Unit Sphere" (2014). HMC Senior Theses. 62.