Topological Methods For Ordinary Differential Equations

Author : Patrick Fitzpatrick,Mario Martelli,Jean Mawhin,Roger Nussbaum
Publisher : Springer
Page : 223 pages
File Size : 48,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540475637

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Topological Methods for Ordinary Differential Equations by Patrick Fitzpatrick,Mario Martelli,Jean Mawhin,Roger Nussbaum Pdf

The 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.

Author : Centro internazionale matematico estivo. Session
Publisher : Unknown
Page : 218 pages
File Size : 42,6 Mb
Release : 1993
Category : Electronic
ISBN : OCLC:1132166895

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Topological Methods for Ordinary Differential Equations by Centro internazionale matematico estivo. Session Pdf

Author : Andrzej Granas,Marlène Frigon
Publisher : Springer Science & Business Media
Page : 531 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103398

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Topological Methods in Differential Equations and Inclusions by Andrzej Granas,Marlène Frigon Pdf

The 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.

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 430 pages
File Size : 43,7 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822612

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological 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.

Author : Pablo Amster
Publisher : Springer
Page : 244 pages
File Size : 49,7 Mb
Release : 2013-11-30
Category : Electronic
ISBN : 146148894X

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Topological Methods in the Study of Boundary Value Problems by Pablo Amster Pdf

This graduate-level textbook presents representative problems in nonlinear analysis by topological methods. The approach is elementary with simple model equations and applications, allowing students to focus on the application of topological methods.

Author : Jane Cronin
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 53,8 Mb
Release : 1995-01-05
Category : Fixed point theory
ISBN : 9780821815113

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Fixed points and topological degree in nonlinear analysis by Jane Cronin Pdf

The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with ``large'' nonlinearities. Then, after being extended to infinite-dimensional ``function-spaces'', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.

Author : V. Benci,G. Cerami,M. Degiovanni,D. Fortunato,F. Giannoni,A.M. Micheletti
Publisher : Springer Science & Business Media
Page : 133 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200819

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Variational and Topological Methods in the Study of Nonlinear Phenomena by V. Benci,G. Cerami,M. Degiovanni,D. Fortunato,F. Giannoni,A.M. Micheletti Pdf

This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. A broad range of topics is covered, including: * concentration phenomena in pdes * variational methods with applications to pdes and physics * periodic solutions of odes * computational aspects in topological methods * mathematical models in biology Though well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors: M. Clapp, M. Del Pino, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Séré, E. Schwartzman, P. Sintzoff, R. Turner , M. Willem.

Author : Pablo Amster,Pierluigi Benevieri
Publisher : Birkhäuser
Page : 0 pages
File Size : 53,6 Mb
Release : 2024-09-25
Category : Mathematics
ISBN : 3031613368

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Topological Methods for Delay and Ordinary Differential Equations by Pablo Amster,Pierluigi Benevieri Pdf

This 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.

Author : Yihong Du
Publisher : World Scientific
Page : 202 pages
File Size : 43,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812566249

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Order Structure and Topological Methods in Nonlinear Partial Differential Equations by Yihong Du Pdf

The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.

Author : Yihong Du
Publisher : World Scientific
Page : 202 pages
File Size : 46,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812774446

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Order Structure and Topological Methods in Nonlinear Partial Differential Equations by Yihong Du Pdf

The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems. The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time. Sample Chapter(s). Chapter 1: Krein-Rutman Theorem and the Principal Eigenvalue (128 KB). Contents: KreinOCoRutman Theorem and the Principal Eigenvalue; Maximum Principles Revisited; The Moving Plane Method; The Method of Upper and Lower Solutions; The Logistic Equation; Boundary Blow-Up Problems; Symmetry and Liouville Type Results Over Half and Entire Spaces. Readership: Researchers and postgraduate students in partial differential equations."

Author : V.V. Filippov
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401708418

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Basic Topological Structures of Ordinary Differential Equations by V.V. Filippov Pdf

The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist.

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 43,7 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 1402032218

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Handbook of Topological Fixed Point Theory by Robert F. Brown Pdf

This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Author : Zhitao Zhang
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 54,7 Mb
Release : 2012-09-17
Category : Mathematics
ISBN : 9783642307096

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Variational, Topological, and Partial Order Methods with Their Applications by Zhitao Zhang Pdf

Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.

Author : Guglielmo Feltrin
Publisher : Springer
Page : 304 pages
File Size : 53,5 Mb
Release : 2018-11-23
Category : Mathematics
ISBN : 9783319942384

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Positive Solutions to Indefinite Problems by Guglielmo Feltrin Pdf

This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that compelling and substantial research can be obtained and presented in a penetrable way. In particular, the book focuses on second order nonlinear differential equations. It analyzes the Dirichlet, Neumann and periodic boundary value problems associated with the equation and provides existence, nonexistence and multiplicity results for positive solutions. The author proposes a new approach based on topological degree theory that allows him to answer some open questions and solve a conjecture about the dependence of the number of positive solutions on the nodal behaviour of the nonlinear term of the equation. The new technique developed in the book gives, as a byproduct, infinitely many subharmonic solutions and globally defined positive solutions with chaotic behaviour. Furthermore, some future directions for research, open questions and interesting, unexplored topics of investigation are proposed.

Author : Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 46,7 Mb
Release : 2013-11-19
Category : Mathematics
ISBN : 9781461493235

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Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems by Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou Pdf

This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.