On Leighton's Comparison Theorem
Classical Analysis and ODEs
2017-03-22 v1
Abstract
We give a simple proof of a fairly flexible comparison theorem for equations of the type on a finite interval where , , , and are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schr\"odinger equations with distributional potentials as well as Jacobi difference equations.
Cite
@article{arxiv.1703.06949,
title = {On Leighton's Comparison Theorem},
author = {Ahmed Ghatasheh and Rudi Weikard},
journal= {arXiv preprint arXiv:1703.06949},
year = {2017}
}