Mathematical Sciences: Boundary Layer Phenomena for Functional Differential Equations and Means and Their Iterations

点击翻译按钮获取中文摘要

This project continues work on the mathematical theory of functional differential equations. Of particular interest are those equations involving time delay and the presence of a negative feed-back condition. Singular perturbation methods will be employed. Equations of this type arise in a number of applications such as optics, physiology and mathematical biology. Considerable progress has been made on these equations. Emphasis will be placed on understanding the dynamics of solutions having prescribed values given over an interval. A particular instance would be to give conditions for the existence of slowly varying solutions. Other work will focus on equations where one has state dependent time lags which model blood cell production and agricultural commodity cycles. Here again, one looks for periodicity properties of solutions as well as insight into the asymptotic properties of solutions as the perturbation parameter tends to zero. Another class of problems to be considered involves functional differential equations where the forcing functional depends on the delayed values of the solution as well as the current values. Here the primary object is to determine if there are no nonconstant solutions of period equal to four. Examples indicate that this conjecture is true, although its validity is by no means assured.