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

摘要

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 oscillatoryonoscillatory when the parameter is on the oscillation constant. We also show an application to singular elliptic eigenvalue problems on a ball in RN.