Author: Publisher: Academic Press
ISBN: 0080873456
Category : Mathematics
Languages : en
Pages : 405
Book Description
Critical Point Theory in Global Analysis and Differential Topology
Critical Point Theory in Global Analysis and Differential Topology
Author: Publisher: Academic Press
ISBN: 0080873456
Category : Mathematics
Languages : en
Pages : 405
Book Description
Critical Point Theory in Global Analysis and Differential Topology
Critical Point Theory in Global Analysis and Differential Topology
Author: Research in Progress
Author: Differential Topology
Author: Victor GuilleminPublisher: American Mathematical Soc.
ISBN: 0821851934
Category : Mathematics
Languages : en
Pages : 242
Book Description
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
Library of Congress Subject Headings
Author: Library of CongressPublisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1432
Book Description
Library of Congress Subject Headings
Author: Library of Congress. Cataloging Policy and Support OfficePublisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1688
Book Description
Library of Congress Subject Headings
Author: Library of Congress. Subject Cataloging DivisionPublisher:
ISBN:
Category : Subject headings
Languages : en
Pages : 1326
Book Description
Topological Methods in Differential Equations and Inclusions
Author: Andrzej GranasPublisher: Springer Science & Business Media
ISBN: 9401103399
Category : Mathematics
Languages : en
Pages : 531
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.
Critical Point Theory
Author: Martin SchechterPublisher: Springer Nature
ISBN: 303045603X
Category : Mathematics
Languages : en
Pages : 347
Book Description
This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book’s main subject: applications to problems in mathematics and physics. These include topics such as Schrödinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.
A-E
Author: Library of Congress. Office for Subject Cataloging PolicyPublisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1548
Book Description