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

Author

Emily M. Fischer, Harvey Mudd CollegeFollow

Graduation Year

2014

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Alfonso Castro

Reader 2

Weiqing Gu

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2014 Emily Fischer

Abstract

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.

Recommended Citation

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.
https://scholarship.claremont.edu/hmc_theses/62