Date of Award

2009

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Basant Karna

Second Advisor

Bonita Lawrence

Third Advisor

Judith Silver

Abstract

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary value problem for a dynamic equation where the domain of the unknown function is a so called time scale, an arbitrary nonempty closed subset of the reals.

Subject(s)

Differential equations.

Difference equations.

Differentiable dynamical systems.