Improvements of Dynamic Opial-Type Inequalities and Applications

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Ramy R. Mahmoud
Samir H. Saker

Abstract

In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently introduced new technique for Opial dynamic inequalities, the time scales integration by parts formula, the time scales chain rule, the time scales Taylor formula, and classical as well as time scales versions of Hölder's inequality.

Recommended Citation

M. Bohner et al., "Improvements of Dynamic Opial-Type Inequalities and Applications," Dynamic Systems and Applications, vol. 24, no. 1-2, pp. 229 - 241, Dynamic Publishers, Jan 2015.

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1056-2176

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Dynamic Publishers, All rights reserved.

Publication Date

01 Jan 2015