Linear and Nonlinear Non-Fredholm Operators - Messoud Efendiev

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Auteur(s) : Messoud Efendiev

Editeur : Springer Singapore

Langue : Anglais

Parution : 01/02/2024

Format : Moyen, de 350g à 1kg

Nombre de pages : 224

Expédition : 347

Dimensions : 23.5 x 15.5 x 1.3

ISBN : 9811998825

Résumé :

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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Biographie:
Professor Messoud Efendiev has been a major player and scientific leader in the field of infinite dimensional dynamical systems with applications to the life sciences, especially in biology, medicine and ecology. He has an extensive international collaborative network, formed during his graduate training at the Lomonosov Moscow State University, his AvH Fellowship at the University of Stuttgart, his postdoctoral studies at the Freie Universit?t Berlin, and his further career, including at the DFG Collaborative Research Center and the Helmholtz Center Munich. He is the recipient of various international fellowships and awards from Japan and Europe and has been a much sought-after speaker at major international research colloquia and conferences. Professor Efendiev was the first Azerbaijani scientist to be awarded the prestigious Feodor Lynen Research Fellowship for experienced researchers by the Alexander von Humboldt Foundation. He has collaborated with many distinguished mathematicians in many countries. In 2018 he held the Dean's Distinguished Visiting Professorship, a joint program of the Fields Institute with the Faculty of Arts and Science and the Department of Mathematics at the University of Toronto....