"This dissertation consists of five papers in which discrete Volterra equations of different types and orders are studied and results regarding the behavior of their solutions are established. The first paper presents some fundamental results about subexponential sequences. It also illustrates the subexponential solutions of scalar linear Volterra sum-difference equations are asymptotically stable. The exact value of the rate of convergence of asymptotically stable solutions is found by determining the asymptotic behavior of the transient renewal equations. The study of subexponential solutions is also continued in the second and third articles. The second paper investigates the same equation using the same process as considered in the first paper. The discussion focuses on a positive lower bound of the rate of convergence of the asymptotically stable solutions. The third paper addresses the rate of convergence of the solutions of scalar linear Volterra sum-difference equations with delay. The result is proved by developing the rate of convergence of transient renewal delay difference equations. The fourth paper discusses the existence of bounded solutions on an unbounded domain of more general nonlinear Volterra sum-difference equations using the Schaefer fixed point theorem and the Lyapunov direct method. The fifth paper examines the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations and establishes some new criteria based on so-called time scales, which unifies and extends both discrete and continuous mathematical analysis. Beside these five research papers that focus on discrete Volterra equations, this dissertation also contains an introduction, a section on difference calculus, a section on time scales calculus, and a conclusion."--Abstract, page v.
Bohner, Martin, 1966-
Clark, Stephen L.
Le, Vy Khoi
Gelles, Gregory M.
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
Journal article titles appearing in thesis/dissertation
- Subexponential solutions of linear Volterra difference equations
- Rate of convergence of solutions of linear Volterra difference equations
- Subexponential solutions of linear Volterra delay difference equations
- Bounded solutions of a Volterra difference equation
- Asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations
x, 121 pages
© 2015 Nasrin Sultana, All rights reserved.
Dissertation - Open Access
Difference equations -- Analysis
Electronic OCLC #
Link to Catalog Record
Sultana, Nasrin, "Volterra difference equations" (2015). Doctoral Dissertations. 2396.