Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems

Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems
Author :
Publisher : American Mathematical Soc.
Total Pages : 145
Release :
ISBN-10 : 9780821825440
ISBN-13 : 0821825445
Rating : 4/5 (40 Downloads)

Synopsis Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems by : Patrick Fitzpatrick

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

Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems
Author :
Publisher : American Mathematical Society(RI)
Total Pages : 145
Release :
ISBN-10 : 147040060X
ISBN-13 : 9781470400606
Rating : 4/5 (0X Downloads)

Synopsis Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems by : Patrick Fitzpatrick

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.

Nonlinear Elliptic and Parabolic Problems

Nonlinear Elliptic and Parabolic Problems
Author :
Publisher : Springer Science & Business Media
Total Pages : 531
Release :
ISBN-10 : 9783764373856
ISBN-13 : 3764373857
Rating : 4/5 (56 Downloads)

Synopsis Nonlinear Elliptic and Parabolic Problems by : Michel Chipot

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

Generalized Topological Degree and Semilinear Equations
Author :
Publisher : Cambridge University Press
Total Pages : 252
Release :
ISBN-10 : 9780521444743
ISBN-13 : 0521444748
Rating : 4/5 (43 Downloads)

Synopsis Generalized Topological Degree and Semilinear Equations by : Wolodymyr V. Petryshyn

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

Topological Nonlinear Analysis II
Author :
Publisher : Springer Science & Business Media
Total Pages : 609
Release :
ISBN-10 : 9781461241263
ISBN-13 : 146124126X
Rating : 4/5 (63 Downloads)

Synopsis Topological Nonlinear Analysis II by : Michele Matzeu

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

Mathematical Modelling of Industrial Processes
Author :
Publisher : Springer
Total Pages : 166
Release :
ISBN-10 : 9783540472476
ISBN-13 : 3540472479
Rating : 4/5 (76 Downloads)

Synopsis Mathematical Modelling of Industrial Processes by : Stavros Busenberg

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

Weakly Nonlinear Dirichlet Problems on Long or Thin Domains
Author :
Publisher : American Mathematical Soc.
Total Pages : 81
Release :
ISBN-10 : 9780821825631
ISBN-13 : 0821825631
Rating : 4/5 (31 Downloads)

Synopsis Weakly Nonlinear Dirichlet Problems on Long or Thin Domains by : Edward Norman Dancer

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

Nonlinear Problems of Elasticity
Author :
Publisher : Springer Science & Business Media
Total Pages : 845
Release :
ISBN-10 : 9780387276496
ISBN-13 : 0387276491
Rating : 4/5 (96 Downloads)

Synopsis Nonlinear Problems of Elasticity by : Stuart Antman

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

Topological Methods for Ordinary Differential Equations

Topological Methods for Ordinary Differential Equations
Author :
Publisher : Springer
Total Pages : 223
Release :
ISBN-10 : 9783540475637
ISBN-13 : 354047563X
Rating : 4/5 (37 Downloads)

Synopsis Topological Methods for Ordinary Differential Equations by : Patrick Fitzpatrick

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.

Manifolds with Group Actions and Elliptic Operators

Manifolds with Group Actions and Elliptic Operators
Author :
Publisher : American Mathematical Soc.
Total Pages : 90
Release :
ISBN-10 : 9780821826041
ISBN-13 : 0821826042
Rating : 4/5 (41 Downloads)

Synopsis Manifolds with Group Actions and Elliptic Operators by : Vladimir I︠A︡kovlevich Lin

This work studies equivariant linear second order elliptic operators [italic capital]P on a connected noncompact manifold [italic capital]X with a given action of a group [italic capital]G. The action is assumed to be cocompact, meaning that [italic capitals]GV = [italic capital]X for some compact subset of [italic capital]V of [italic capital]X. The aim is to study the structure of the convex cone of all positive solutions of [italic capital]P[italic]u = 0.