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Because the theory of equations with delay terms occurs in a
variety of contexts, it is important to provide a framework,
whenever possible, to handle as many cases as possible
simultaneously so as to bring out a better insight and
understanding of the subtle differences of the various equations
with delays. Furthermore, such a unified theory would avoid
duplication and expose open questions that are significant for
future research. It is in this spirit that the authors view the
importance of their monograph, which presents a systematic and
unified theory of recent developments of equations with unbounded
delay, describes the current state of the theory showing the
essential unity achieved, and provides a general structure
applicable to a variety of problems. It is the first book that: (i)
presents a unified framework to investigate the basic existence
theory for a variety of equations with delay; (ii) treats the
classification of equations with memory precisely so as to bring
out the subtle differences between them; (iii) develops a
systematic study of stability theory in terms of two different
measures which includes several known concepts; and (iv) exhibits
the advantages of employing Lyapunov functions on product spaces as
well as the method of perturbing Lyapunov functions. This book will
be of value to researchers and advanced graduate students in
mathematics, electrical engineering and biomathematics.
Because the theory of equations with delay terms occurs in a
variety of contexts, it is important to provide a framework,
whenever possible, to handle as many cases as possible
simultaneously so as to bring out a better insight and
understanding of the subtle differences of the various equations
with delays. Furthermore, such a unified theory would avoid
duplication and expose open questions that are significant for
future research. It is in this spirit that the authors view the
importance of their monograph, which presents a systematic and
unified theory of recent developments of equations with unbounded
delay, describes the current state of the theory showing the
essential unity achieved, and provides a general structure
applicable to a variety of problems. It is the first book that: (i)
presents a unified framework to investigate the basic existence
theory for a variety of equations with delay; (ii) treats the
classification of equations with memory precisely so as to bring
out the subtle differences between them; (iii) develops a
systematic study of stability theory in terms of two different
measures which includes several known concepts; and (iv) exhibits
the advantages of employing Lyapunov functions on product spaces as
well as the method of perturbing Lyapunov functions. This book will
be of value to researchers and advanced graduate students in
mathematics, electrical engineering and biomathematics.
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