Nonlinear Integral Equations in Abstract Spaces (Mathematics and Its Applications)

Guo, Dajun; Lakshmikantham, V.; Xinzhi Liu

ISBN 10: 146128547X / ISBN 13: 9781461285472

Editore: Springer, 2013

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Dati bibliografici

• Titolo: Nonlinear Integral Equations in Abstract Spaces (Mathematics and Its Applications)
• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 146128547X
• ISBN 13: 9781461285472
• Rilegatura: Brossura
• Condizione: New

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Riassunto

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.

Contenuti

Preface. 1. Preliminaries. 2. Nonlinear Integral Equations in Banach Spaces. 3. Nonlinear Integro-Differential Equations in Banach Spaces. 4. Nonlinear Impulsive Integral Equations in Banach Spaces. References.