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Many problems arising in the physical sciences, engineering,
biology and ap plied mathematics lead to mathematical models
described by nonlinear integral equations in abstract spaces. The
theory of nonlinear integral equations in ab stract spaces is a
fast growing field with important applications to a number of areas
of analysis as well as other branches of science. This book is
devoted to a comprehensive treatment of nonlinear integral
equations in abstract spaces. It is the first book that is
dedicated to a systematic development of this subject, and it
includes the developments during recent years. Chapter 1 introduces
some basic results in analysis, which will be used in later
chapters. Chapter 2, which is a main portion of this book, deals
with nonlin ear integral equations in Banach spaces, including
equations of Fredholm type, of Volterra type and equations of
Hammerstein type. Some applica equations tions to nonlinear
differential equations in Banach spaces are given. We also discuss
an integral equation modelling infectious disease as a typical
applica tion. In Chapter 3, we investigate the first order and
second order nonlinear integro-differential equations in Banach
spaces including equations of Volterra type and equations of mixed
type. Chapter 4 is devoted to nonlinear impulsive integral
equations in Banach spaces and their applications to nonlinear
impul sive differential equations in Banach spaces."
Many problems arising in the physical sciences, engineering,
biology and ap plied mathematics lead to mathematical models
described by nonlinear integral equations in abstract spaces. The
theory of nonlinear integral equations in ab stract spaces is a
fast growing field with important applications to a number of areas
of analysis as well as other branches of science. This book is
devoted to a comprehensive treatment of nonlinear integral
equations in abstract spaces. It is the first book that is
dedicated to a systematic development of this subject, and it
includes the developments during recent years. Chapter 1 introduces
some basic results in analysis, which will be used in later
chapters. Chapter 2, which is a main portion of this book, deals
with nonlin ear integral equations in Banach spaces, including
equations of Fredholm type, of Volterra type and equations of
Hammerstein type. Some applica equations tions to nonlinear
differential equations in Banach spaces are given. We also discuss
an integral equation modelling infectious disease as a typical
applica tion. In Chapter 3, we investigate the first order and
second order nonlinear integro-differential equations in Banach
spaces including equations of Volterra type and equations of mixed
type. Chapter 4 is devoted to nonlinear impulsive integral
equations in Banach spaces and their applications to nonlinear
impul sive differential equations in Banach spaces."
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