Generalized Solutions Of Functional Differential Equations

This book addresses the nedd for investigation of functional differential equations with discontinuous delays. Such equations provide a mathematical model for a physical or biological system in which the rate of change of the system depends upon its past history. Work is described that has been done by the author and others over thelast few years on differential equations with piecewise continuous arguments (EPCA). They include, as particular cases, impulse and loaded equations of control theory and are similar in structure to those found in certain sequential-continuous models of disease dynamics. Considerable attention is given to the study of initial and boundary-value problems for partial differential equations of mathematical physic with discontinuous time delays. A large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. In each of the directions discussed in this book, there appears to be ample opportunity for extending the known results.