Theory Of Differential Equations With Unbounded Delay (mathematics And Its Applications)
by V. Lakshmikantham /
2013 / English / PDF
16.9 MB Download
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.
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 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:
It is the first book that:
(i) presents a unified framework to investigate the basic existence
theory for a variety of equations with delay;
(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;
(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
(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.
(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.
This book will be of value to researchers and advanced graduate
students in mathematics, electrical engineering and
biomathematics.
