Doctoral Dissertations

Keywords and Phrases

Classifications; Dynamical systems on time scales; Dynamic equations on time scales; Nonoscillation; Time Scales; Time Scale Systems

Abstract

"During the past years, there has been an increasing interest in studying oscillation and nonoscillation criteria for dynamic equations and systems on time scales that harmonize the oscillation and nonoscillation theory for the continuous and discrete cases in order to combine them in one comprehensive theory and eliminate obscurity from both.

We not only classify nonoscillatory solutions of dynamic equations and systems on time scales but also guarantee the (non)existence of such solutions by using the Knaster fixed point theorem, Schauder - Tychonoff fixed point theorem, and Schauder fixed point theorem. The approach is based on the sign of nonoscillatory solutions. A short introduction to the time scale calculus is given as well.

Examples are significant in order to see if nonoscillatory solutions exist or not. Therefore, we give several examples in order to highlight our main results for the set of real numbers R, the set of integers Z, and qN0 = {1, q, q2, q3, ...}, q > 1, which are the most well-known time scales"--Abstract, page iv.

Advisor(s)

Akin, Elvan

Committee Member(s)

Bohner, Martin, 1966-
Grow, David E.
Singler, John R.
Gelles, Gregory M

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2016

Journal article titles appearing in thesis/dissertation

  • Classification of nonoscillatory solutions of nonlinear dynamic equations on time scales
  • On nonoscillatory solutions of emden-fowler dynamic systems on time scales
  • Nonoscillation criteria for two-dimensional time-scale systems
  • On nonoscillatory solutions of two dimensional nonlinear time scale systems with delay

Pagination

x, 120 pages)

Note about bibliography

Includes bibliographic references.

Rights

© 2016 Özkan Özturk, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Differentiable dynamical systems
Difference equations

Thesis Number

T 10922

Electronic OCLC #

952597934

Included in

Mathematics Commons

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