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AuthorGuo, Dajun. author
TitleNonlinear Integral Equations in Abstract Spaces [electronic resource] / by Dajun Guo, V. Lakshmikantham, Xinzhi Liu
ImprintBoston, MA : Springer US : Imprint: Springer, 1996
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Descript VIII, 344 p. online resource


Many problems arising in the physical sciences, engineering, biology and apยญ plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in abยญ 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 nonlinยญ ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applicaยญ equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applicaยญ 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 impulยญ sive differential equations in Banach spaces

Mathematics Functional analysis Integral equations Operator theory Differential equations Mathematics Integral Equations Ordinary Differential Equations Functional Analysis Operator Theory


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