Harnack’s inequality for second order linear ordinary differential inequalities

Mohammed, Ahmed; Turner, Hannah

doi:10.2140/involve.2016.9.281

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Harnack's inequality for second order linear ordinary differential inequalities

Ahmed Mohammed and Hannah Turner

Vol. 9 (2016), No. 2, 281–292

DOI: 10.2140/involve.2016.9.281

Abstract

We prove a Harnack-type inequality for nonnegative solutions of second order ordinary differential inequalities. Maximum principles are the main tools used, and to make the paper self-contained, we provide alternative proofs to those available in the literature.

Keywords

Harnack's inequality, maximum principles, ordinary differential inequalities

Mathematical Subject Classification 2010

Primary: 34C11

Milestones

Received: 28 October 2014

Revised: 26 February 2015

Accepted: 4 March 2015

Published: 2 March 2016

Communicated by Johnny Henderson

Authors

Ahmed Mohammed
Department of Mathematical Sciences Ball State University Muncie, IN 47306 United States

Hannah Turner
Department of Mathematical Sciences Ball State University Muncie, IN 47306 United States

Vol. 9, No. 2, 2016