Bonita A. Lawrence

An existence result for a multipoint boundary value problem on a time scale

We will expand the scope of application of a fixed point theorem due to Krasnoselskiĭ and Zabreiko to the family of second-order dynamic equations described by uΔΔ(t) = f(uσ(t)), , with multipoint boundary conditions u(0) = 0, , and for the purpose of establishing existence results. We will determine sufficient conditions on our function f such that the assumptions of the fixed point theorem are satisfied, which in return gives us the existence of solutions.

Almost oscillatory three-dimensional dynamical system

In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.2010 Mathematics Subject Classification: 39A10

A variety of differentiability results for a multi-point boundary value problem

The goal of this work is to address differentiability of solutions of a nonlinear dynamic system with multi-point boundary conditions described by xΔ = f(t, x), Σm=1k Mmx(tm) = r, where r ∈ Rn and, for each 1 ≤ m ≤ k, Mm is an n × n constant matrix and tm ∈ T. The solution of this system is defined on a measure chain, T, and xΔ denotes a generalized derivative known as the delta derivative.

On joint probability density functions of discrete time iterative processes

In this work, we develop an algorithm for determining the marginal probability density function of the solution processes of a nonlinear non-stationary discrete time iterative process with random parameters. The results include the case of degenerate random initial states. As a by-product of our study, the special case when the initial state is non-degenerate is addressed.

Topological Structures for Studying Dynamic Equations on Time Scales

We construct the topological framework within which we can study the solution space for a given dynamic equation on time scales. We call these the Hausdorff-Fell topologies. The space of finite time scales is dense in the space of all time scales under the Hausdorff-Fell topology. The natural projection from solutions to their domains is a homeomorphism when all solutions are unique.