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Author: Patrick Fitzpatrick
Publisher: Springer
ISBN: 354047563X
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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: Patrick Fitzpatrick
Publisher: Springer
ISBN: 354047563X
Category : Mathematics
Languages : en
Pages : 223
Get Book Here
Book Description
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: Andrzej Granas
Publisher: Springer Science & Business Media
ISBN: 9401103399
Category : Mathematics
Languages : en
Pages : 531
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Book Description
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: Centro internazionale matematico estivo. Session
Publisher:
ISBN:
Category :
Languages : en
Pages : 218
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Book Description
Author: Jane Cronin
Publisher:
ISBN:
Category : Fixed point theory
Languages : en
Pages : 220
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Book Description
Author: John R. Graef
Publisher: CRC Press
ISBN: 0429822626
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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 Nature
ISBN: 3031613376
Category :
Languages : en
Pages : 220
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Book Description
Author: V.V. Filippov
Publisher: Springer Science & Business Media
ISBN: 940170841X
Category : Mathematics
Languages : en
Pages : 536
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Book Description
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: V. Benci
Publisher: Springer Science & Business Media
ISBN: 9780817642785
Category : Mathematics
Languages : en
Pages : 152
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Book Description
The articles in this volume are an outgrowth of an international conference entitled Variational and Topological Methods in the Study of Nonlinear Phe- nomena, held in Pisa in January-February 2000. Under the framework of the research project Differential Equations and the Calculus of Variations, the conference was organized to celebrate the 60th birthday of Antonio Marino, one of the leaders of the research group and a significant contrib- utor to the mathematical activity in this area of nonlinear analysis. The volume highlights 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 meth- ods. A broad range of topics is covered, including: concentration phenomena in PDEs, variational methods with applications to PDEs and physics, pe- riodic solutions of ODEs, computational aspects in topological methods, and mathematical models in biology. Though well-differentiated, the topics covered are unified through a com- mon 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 are M. Clapp, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzan- towicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, M. del Pino, E. Sere, E. Schwartzman, P. Sintzoff, R. Turner, and I\f. Willem.
Author:
Publisher:
ISBN:
Category : Nonlinear functional analysis
Languages : en
Pages : 412
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Book Description
Author: Zhitao Zhang
Publisher: Springer Science & Business Media
ISBN: 3642307086
Category : Mathematics
Languages : en
Pages : 333
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Book Description
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.
