Almost Periodic Type Solutions
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Almost Periodic Type Solutions
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodic Type Solutions written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
Maybe for the first time in the existing literature, we investigate here the almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also investigate the generalized almost periodic type sequences and their applications in a rather detailed manner as well as many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions. We essenitally apply some results from the theory of C-regularized solution operator families to the abstract Volterra integro-differential-difference equations, contributing also to the theory of fractional calculus and fractional differential equations. The theory of abstract Volterra integro-differential equations and the theory of abstract Volterra difference equations are very attractive fields of research of many authors. The almost periodic features and the asymptotically almost periodic features of solutions to the abstract Volterra differential-difference equations in Banach spaces have been sought in many research articles published by now. The main aim of this monograph is to continue the work collected in my monographs published with W. de Gruyter recently by providing several new results about the existence and uniqueness of almost periodic type solutions to the abstract Volterra integro-differential-difference equations which could be solvable or unsolvable with respect to the highest derivative (order). We would like to particularly emphasize that this is probably the first research monograph devoted to the study of almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also consider here many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions, and their almost automorphic analogues. It is also worth noting that this is probably the first research monograph which concerns the generalized almost periodic type sequences and their applications in a rather detailed manner; for the first time in the existing literature, we also present here some applications of results from the theory of $C$-regularized solution operator families to the abstract Volterra difference equations. Fractional calculus and discrete fractional calculus are rapidly growing fields of theoretical and applied mathematics, which are incredibly important in modeling of various real phenomena appearing in different fields like aerodynamics, rheology, interval-valued systems, chaotic systems with short memory and image encryption and discrete-time recurrent neural networks. Many important research results regarding the abstract fractional differential equations and the abstract fractional difference equations in Banach spaces have recently been obtained by a great number of authors from the whole world. In this monograph, we also contribute to the theories of (discrete) fractional calculus, fractional differential-difference equations and multi-dimensional Laplace transform. Although the monograph is far from being complete, we have decided to quote almost eight hundred and fifty research articles which could be of some importance to the interested readers for further developments of the theory established here.
Almost Periodic Type Functions And Ergodicity
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Author : Zhang Chuanyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-30
Almost Periodic Type Functions And Ergodicity written by Zhang Chuanyi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Mathematics categories.
The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.
Almost Periodic Type Solutions
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodic Type Solutions written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
Maybe for the first time in the existing literature, we investigate here the almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also investigate the generalized almost periodic type sequences and their applications in a rather detailed manner as well as many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions. We essenitally apply some results from the theory of C-regularized solution operator families to the abstract Volterra integro-differential-difference equations, contributing also to the theory of fractional calculus and fractional differential equations. The theory of abstract Volterra integro-differential equations and the theory of abstract Volterra difference equations are very attractive fields of research of many authors. The almost periodic features and the asymptotically almost periodic features of solutions to the abstract Volterra differential-difference equations in Banach spaces have been sought in many research articles published by now. The main aim of this monograph is to continue the work collected in my monographs published with W. de Gruyter recently by providing several new results about the existence and uniqueness of almost periodic type solutions to the abstract Volterra integro-differential-difference equations which could be solvable or unsolvable with respect to the highest derivative (order). We would like to particularly emphasize that this is probably the first research monograph devoted to the study of almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also consider here many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions, and their almost automorphic analogues. It is also worth noting that this is probably the first research monograph which concerns the generalized almost periodic type sequences and their applications in a rather detailed manner; for the first time in the existing literature, we also present here some applications of results from the theory of $C$-regularized solution operator families to the abstract Volterra difference equations. Fractional calculus and discrete fractional calculus are rapidly growing fields of theoretical and applied mathematics, which are incredibly important in modeling of various real phenomena appearing in different fields like aerodynamics, rheology, interval-valued systems, chaotic systems with short memory and image encryption and discrete-time recurrent neural networks. Many important research results regarding the abstract fractional differential equations and the abstract fractional difference equations in Banach spaces have recently been obtained by a great number of authors from the whole world. In this monograph, we also contribute to the theories of (discrete) fractional calculus, fractional differential-difference equations and multi-dimensional Laplace transform. Although the monograph is far from being complete, we have decided to quote almost eight hundred and fifty research articles which could be of some importance to the interested readers for further developments of the theory established here.
Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-05-06
Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with Mathematics categories.
This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.
Selected Topics In Almost Periodicity
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Selected Topics In Almost Periodicity written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
Metrical Almost Periodicity And Applications To Integro Differential Equations
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-06-06
Metrical Almost Periodicity And Applications To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.
The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.
Almost Periodicity And Almost Automorphy
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Author : Abdallah Afoukal
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodicity And Almost Automorphy written by Abdallah Afoukal and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces
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Author : Toka Diagana
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces written by Toka Diagana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.
Differential Equations And Nonlinear Mechanics
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Author : Kuppalapalle Vajravelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Differential Equations And Nonlinear Mechanics written by Kuppalapalle Vajravelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Aerospace Engineering, and the Office of International Studies (of the University of Central Florida) for the financial support of the conference. Also, to the Mathematics Department of the University of Central Florida for providing secretarial and administrative assistance. I would like to thank the members of the local organizing committee, Jeanne Blank, Jackie Callahan, John Cannon, Holly Carley, Brad Pyle, Pete Rautenstrauch, and June Wingler for their assistance. Thanks are also due to the conference organizing committee, F. H. Busse, J. R. Cannon, V. Girault, R. H. J. Grimshaw, P. N. Kaloni, V.
Informatics And Management Science Iii
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Author : Wenjiang Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-27
Informatics And Management Science Iii written by Wenjiang Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-27 with Technology & Engineering categories.
The International Conference on Informatics and Management Science (IMS) 2012 will be held on November 16-19, 2012, in Chongqing, China, which is organized by Chongqing Normal University, Chongqing University, Shanghai Jiao Tong University, Nanyang Technological University, University of Michigan, Chongqing University of Arts and Sciences, and sponsored by National Natural Science Foundation of China (NSFC). The objective of IMS 2012 is to facilitate an exchange of information on best practices for the latest research advances in a range of areas. Informatics and Management Science contains over 600 contributions to suggest and inspire solutions and methods drawing from multiple disciplines including: Computer Science Communications and Electrical Engineering Management Science Service Science Business Intelligence