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arXiv · 1703.06949

On Leighton's Comparison Theorem

Ahmed Ghatasheh·Rudi Weikard
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Abstract

We give a simple proof of a fairly flexible comparison theorem for equations of the type $-(p(u'+su))'+rp(u'+su)+qu=0$ on a finite interval where $1/p$, $r$, $s$, and $q$ 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.

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BibTeXRIS

Ahmed Ghatasheh, Rudi Weikard. 2017-03-20. On Leighton's Comparison Theorem. https://doi.org/10.1016/j.jde.2017.02.026

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