Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems
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Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems
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Author : Patrick Fitzpatrick
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-08-31
Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems written by Patrick Fitzpatrick and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.
The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce parity, a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.
Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems
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Author : Patrick Fitzpatrick
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems written by Patrick Fitzpatrick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce ''parity'', a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.
Orientation And The Leray Schauder Theory For Fully Nonlinear For Fully Nonlinear Elliptic Boundary Value Problems
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Author : Patrick Fitzpatrick
language : en
Publisher:
Release Date : 1993
Orientation And The Leray Schauder Theory For Fully Nonlinear For Fully Nonlinear Elliptic Boundary Value Problems written by Patrick Fitzpatrick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Nonlinear Elliptic And Parabolic Problems
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Author : Michel Chipot
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-09
Nonlinear Elliptic And Parabolic Problems written by Michel Chipot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-09 with Mathematics categories.
Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.
Generalized Topological Degree And Semilinear Equations
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Author : Wolodymyr V. Petryshyn
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-29
Generalized Topological Degree And Semilinear Equations written by Wolodymyr V. Petryshyn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-29 with Mathematics categories.
This book describes many new results and extensions of the theory of generalized topological degree for densely defined A-proper operators and presents important applications, particularly to boundary value problems of nonlinear ordinary and partial differential equations that are intractable under any other existing theory. A-proper mappings arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. The theory subsumes classical theory involving compact vector fields as well as the more recent theories of condensing vector-fields, strongly monotone, and strongly accretive maps. Researchers and graduate students in mathematics, applied mathematics, and physics who make use of nonlinear analysis will find this an important resource for new techniques.
Topological Nonlinear Analysis Ii
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Author : Michele Matzeu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Nonlinear Analysis Ii written by Michele Matzeu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.
Mathematical Modelling Of Industrial Processes
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Author : Stavros Busenberg
language : en
Publisher: Springer
Release Date : 2006-12-08
Mathematical Modelling Of Industrial Processes written by Stavros Busenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The 1990 CIME course on Mathematical Modelling of Industrial Processes set out to illustrate some advances in questions of industrial mathematics, i.e.of the applications of mathematics (with all its "academic" rigour) to real-life problems. The papers describe the genesis of the models and illustrate their relevant mathematical characteristics. Among the themesdealt with are: thermally controlled crystal growth, thermal behaviour of a high-pressure gas-discharge lamp, the sessile-drop problem, etching processes, the batch-coil- annealing process, inverse problems in classical dynamics, image representation and dynamical systems, scintillation in rear projections screens, identification of semiconductor properties,pattern recognition with neural networks. CONTENTS: H.K. Kuiken: Mathematical Modelling of Industrial Processes.- B. Forte: Inverse Problems in Mathematics for Industry.- S. Busenberg: Case Studies in Industrial Mathematics.
Weakly Nonlinear Dirichlet Problems On Long Or Thin Domains
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Author : Edward Norman Dancer
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Weakly Nonlinear Dirichlet Problems On Long Or Thin Domains written by Edward Norman Dancer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
In this paper, we discuss the existence, uniqueness and asymptotic behavior of positive solutions of the equation −[capital Greek]Delta[italic]u = [lowercase Greek]Lambda[function]ƒ([italic]u) in [capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n], [and] [italic]u = 0 on [partial derivative/boundary/degree of a polynomial symbol]([capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n]) for [italic]n large. Here [capital Greek]Omega[surmounted by macron] is a bounded domain in [italic capital]R[superscript italic]k with smooth boundary. Note that by rescaling the equation (including [lowercase Greek]Lambda), our theory covers problems on domains ([set membership symbol][capital Greek]Omega[surmounted by macron]) [times symbol] [−1,1] where [set membership symbol] is small.
Nonlinear Problems Of Elasticity
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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Problems Of Elasticity written by Stuart Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Topological Methods For Ordinary Differential Equations
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Author : Patrick Fitzpatrick
language : en
Publisher: Springer
Release Date : 2006-11-14
Topological Methods For Ordinary Differential Equations written by Patrick Fitzpatrick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.