Convergent Disfocality and Nondisfocality Criteria for Second-Order Linear Differential Equations

Abstract EN

This paper presents a method to determine whether the second-order linear differential equation y′′+q(x)y=0 is either disfocal or nondisfocal in a fixed interval.

The method is based on the recursive application of a linear operator to certain functions and yields upper and lower bounds for the distances between a zero and its adjacent critical points, which will be shown to converge to the exact values of such distances as the recursivity index grows.