Mentor: Dr. Joe Iaia

Title: Two Infinite Families of Solutions of a Singular Differential Equation on Exterior Domains

Abstract: We will establish existence of two infinite families of solutions of a singular differential equation on the exterior of the ball of radius R. After a change of variables this reduces to a study of the ordinary differential equation v'' + h(t) f(v) = 0 on the interval [0,R^{2-N}] with v(0)=0 and v'(0)=a>0. Both of the functions h(t) and f(v) are singular when t=0 which complicates matters. However, the Sturm Comparison Theorem will be a useful tool which will allow us to prove the existence of the two infinite families of solutions.