Topological Methods for Delay and Ordinary Differential Equations
Author: Pablo Amster
Publisher: Springer Nature
Published:
Total Pages: 220
ISBN-13: 3031613376
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Topological Methods for Delay and Ordinary Differential Equations
Author: Pablo Amster
Publisher: Birkhäuser
Published: 2024-09-25
Total Pages: 0
ISBN-13: 9783031613364
DOWNLOAD EBOOKThis volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more. Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats, non-Newtonian fluid flow, and flows in phase space. Topological Methods for Delay and Ordinary Differential Equations will be a valuable resource for researchers interested in differential equations, functional analysis, topology, and the applied sciences.
Topological Methods in Differential Equations and Inclusions
Author: Andrzej Granas
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 531
ISBN-13: 9401103399
DOWNLOAD EBOOKThe papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.
Topological Methods for Ordinary Differential Equations
Author: Patrick Fitzpatrick
Publisher: Springer
Published: 2006-11-14
Total Pages: 223
ISBN-13: 354047563X
DOWNLOAD EBOOKThe volume contains the texts of four courses, given by the authors at a summer school that sought to present the state of the art in the growing field of topological methods in the theory of o.d.e. (in finite and infinitedimension), and to provide a forum for discussion of the wide variety of mathematical tools which are involved. The topics covered range from the extensions of the Lefschetz fixed point and the fixed point index on ANR's, to the theory of parity of one-parameter families of Fredholm operators, and from the theory of coincidence degree for mappings on Banach spaces to homotopy methods for continuation principles. CONTENTS: P. Fitzpatrick: The parity as an invariant for detecting bifurcation of the zeroes of one parameter families of nonlinear Fredholm maps.- M. Martelli: Continuation principles and boundary value problems.- J. Mawhin: Topological degree and boundary value problems for nonlinear differential equations.- R.D. Nussbaum: The fixed point index and fixed point theorems.
Topological Methods for Ordinary Differential Equations
Author: Centro internazionale matematico estivo. Session
Publisher:
Published: 1993
Total Pages: 218
ISBN-13:
DOWNLOAD EBOOKDifferential Equations
Author: Terry E. Moschandreou
Publisher: BoD – Books on Demand
Published: 2018-05-23
Total Pages: 184
ISBN-13: 1789231566
DOWNLOAD EBOOKThe editor has incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis. The authors of each section bring a strong emphasis on theoretical foundations to the book.
Systems with Delays
Author: A. V. Kim
Publisher: John Wiley & Sons
Published: 2015-07-23
Total Pages: 184
ISBN-13: 1119117720
DOWNLOAD EBOOKThe main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays. Referred to as “systems with delays” in this volume, this class of differential equations is also called delay differential equations (DDE), time-delay systems, hereditary systems, and functional differential equations. Delay differential equations are widely used for describing and modeling various processes and systems in different applied problems At present there are effective control and numerical methods and corresponding software for analysis and simulating different classes of ordinary differential equations (ODE) and partial differential equations (PDE). There are many applications for these types of equations, because of this progress, but there are not as many methodologies in systems with delays that are easily applicable for the engineer or applied mathematician. there are no methods of finding solutions in explicit forms, and there is an absence of generally available general-purpose software packages for simulating such systems. Systems with Delays fills this void and provides easily applicable methods for engineers, mathematicians, and scientists to work with delay differential equations in their operations and research.
Delay Equations
Author: Odo Diekmann
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 547
ISBN-13: 1461242061
DOWNLOAD EBOOKThe aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.
Topological Methods for Differential Equations and Inclusions
Author: John R. Graef
Publisher: CRC Press
Published: 2018-09-25
Total Pages: 425
ISBN-13: 0429822618
DOWNLOAD EBOOKTopological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.
Topics in Functional Differential and Difference Equations
Author: Teresa Faria
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 394
ISBN-13: 0821827014
DOWNLOAD EBOOKThis volume contains papers written by participants at the Conference on Functional Differential and Difference Equations held at the Instituto Superior Técnico in Lisbon, Portugal. The conference brought together mathematicians working in a wide range of topics, including qualitative properties of solutions, bifurcation and stability theory, oscillatory behavior, control theory and feedback systems, biological models, state-dependent delay equations, Lyapunov methods, etc. Articles are written by leading experts in the field. A comprehensive overview is given of these active areas of current research. The book will be of interest to both theoretical and applied mathematical scientists.
