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| Author | : Patrick Fitzpatrick |
| Publisher | : Springer |
| Total Pages | : 223 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354047563X |
Download Topological Methods for Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : |
| Total Pages | : 218 |
| Release | : 1993 |
| Genre | : |
| ISBN | : |
Download Topological Methods for Ordinary Differential Equations Book in PDF, ePub and Kindle
| Author | : Andrzej Granas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 531 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401103399 |
Download Topological Methods in Differential Equations and Inclusions Book in PDF, ePub and Kindle
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 |
| Publisher | : CRC Press |
| Total Pages | : 360 |
| Release | : 2018-09-25 |
| Genre | : Mathematics |
| ISBN | : 0429822626 |
Download Topological Methods for Differential Equations and Inclusions Book in PDF, ePub and Kindle
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 |
| Total Pages | : 220 |
| Release | : |
| Genre | : |
| ISBN | : 3031613376 |
Download Topological Methods for Delay and Ordinary Differential Equations Book in PDF, ePub and Kindle
| Author | : V.V. Filippov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 536 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 940170841X |
Download Basic Topological Structures of Ordinary Differential Equations Book in PDF, ePub and Kindle
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 |
| Total Pages | : 133 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200814 |
Download Variational and Topological Methods in the Study of Nonlinear Phenomena Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer |
| Total Pages | : 244 |
| Release | : 2013-11-30 |
| Genre | : |
| ISBN | : 9781461488941 |
Download Topological Methods in the Study of Boundary Value Problems Book in PDF, ePub and Kindle
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. |
| Total Pages | : 212 |
| Release | : 1995-01-05 |
| Genre | : Fixed point theory |
| ISBN | : 0821815113 |
Download Fixed points and topological degree in nonlinear analysis Book in PDF, ePub and Kindle
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 | : Pablo Amster |
| Publisher | : Birkhäuser |
| Total Pages | : 0 |
| Release | : 2024-09-25 |
| Genre | : Mathematics |
| ISBN | : 9783031613364 |
Download Topological Methods for Delay and Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
