Oscillation and nonoscillation theorems for Meissner’s equation

摘要

The purpose of this paper is to present a pair of an oscillation theorem and a nonoscillation theorem for Meissner’s equation which is the special case of Hill’s equation. Proof is given by means of the Riccati technique. Furthermore, using Liouville transformation and Sturm’s comparison theorem, we show a relation between Meissner equations and Cauchy-Euler equations. Moreover, by numerical computations, we give an approximate value which is the borderline between oscillation and nonoscillation for Meissner equations.