Vol. 252, No. 1, 2011

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ISSN: 0030-8730
Some dynamic Wirtinger-type inequalities and their applications

Ravi P. Agarwal, Martin Bohner, Donal O’Regan and Samir H. Saker

Vol. 252 (2011), No. 1, 1–18
Abstract

In this paper, we present some new Wirtinger-type inequalities on time scales. As special cases, some new continuous and discrete Wirtinger-type inequalities are given. The obtained inequalities are applied to a certain class of half-linear dynamic equations on time scales in order to establish sufficient conditions for disconjugacy.

Keywords
Wirtinger-type inequality, dynamic equation, time scale
Mathematical Subject Classification 2000
Primary: 26D10, 26D15, 39A10, 39A12
Milestones
Received: 22 August 2010
Accepted: 28 October 2010
Published: 8 October 2011
Authors
Ravi P. Agarwal
Department of Mathematical Sciences
Texas A&M University – Kingsville
700 University Boulevard
Kingsville, TX 78363-8202
United States
Martin Bohner
Department of Mathematics and Statistics
Missouri University of Science and Technology
400 West 12th Street
Rolla, MO 65409-0020
United States
http://web.mst.edu/~bohner/
Donal O’Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
University Road
Galway
Ireland
http://www.maths.nuigalway.ie/staff/doregan.shtml
Samir H. Saker
Department of Mathematics
King Saud University
Riyadh 11451
Saudi Arabia
http://www.mans.edu.eg/pcvs/30040/