Classification of second-order linear differential equations and an application to singular elliptic eigenvalue problems

Abstract

We consider conditionally oscillatory second-order linear differential equations with a parameter, and investigate the asymptotic behaviour and number of zeros of solutions to the equations. In particular, we find criteria for the equations to be oscillatory/nonoscillatory when the parameter is on the oscillation constant. We also show an application to singular elliptic eigenvalue problems on a ball in RN.