Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 2 (2016), 281-292.

Harnack's inequality for second order linear ordinary differential inequalities

Ahmed Mohammed and Hannah Turner

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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.

Article information

Source
Involve, Volume 9, Number 2 (2016), 281-292.

Dates
Received: 28 October 2014
Revised: 26 February 2015
Accepted: 4 March 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371000

Digital Object Identifier
doi:10.2140/involve.2016.9.281

Mathematical Reviews number (MathSciNet)
MR3470731

Zentralblatt MATH identifier
1341.34015

Subjects
Primary: 34C11: Growth, boundedness

Keywords
Harnack's inequality maximum principles ordinary differential inequalities

Citation

Mohammed, Ahmed; Turner, Hannah. Harnack's inequality for second order linear ordinary differential inequalities. Involve 9 (2016), no. 2, 281--292. doi:10.2140/involve.2016.9.281. https://projecteuclid.org/euclid.involve/1511371000


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References

  • S. Berhanu and A. Mohammed, “A Harnack inequality for ordinary differential equations”, Amer. Math. Monthly 112:1 (2005), 32–41.
  • W. E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems, Wiley, New York, 1965.
  • M. Kassmann, “Harnack inequalities: an introduction”, Bound. Value Probl. (2007), Art. ID 81415.
  • M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Springer, New York, 1984.