Linear and Nonlinear Non-Fredholm Operators: Theory and Applications - Brossura

Efendiev, Messoud

Brossura

ISBN 10: 9811998825 ISBN 13: 9789811998829

Casa editrice: Springer, 2024

Riassunto

This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics.

First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood.

Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.

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Informazioni sull?autore

Dalla quarta di copertina

This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics.

First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood.

Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2024
• Lingua: Inglese
• ISBN 10: 9811998825
• ISBN 13: 9789811998829
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 224
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com