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A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations

Yuji Liu (2009)

Applications of Mathematics

This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation x ' ( t ) = f ( t , x ( t ) , x ( α 1 ( t ) ) , , x ( α n ( t ) ) ) for a.e. t [ 0 , T ] , Δ x ( t k ) = I k ( x ( t k ) ) , k = 1 , , m , x ( 0 ) = x ( T ) . We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin’s continuation theorem. Examples are presented to illustrate the main results.

A Team Approach to Undergraduate Research in Biomathematics: Balance Control

J. Milton, A. Radunskaya, W. Ou, T. Ohira (2011)

Mathematical Modelling of Natural Phenomena

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in–house laboratory component ensures that students have the opportunity...

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