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
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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/