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Author : Renate Schaaf
Publisher : Unknown
Page : 168 pages
File Size : 53,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662176513
Author : Renate Schaaf
Publisher : Springer
Page : 160 pages
File Size : 55,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540467427
The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations.
Author : Herbert B. Keller
Publisher : SIAM
Page : 67 pages
File Size : 54,6 Mb
Release : 1976-01-01
Category : Mathematics
ISBN : 9780898710212
Lectures on a unified theory of and practical procedures for the numerical solution of two point boundary-value problems.
Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 43,6 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828343
Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.
Author : C. De Coster,P. Habets
Publisher : Elsevier
Page : 502 pages
File Size : 43,5 Mb
Release : 2006-03-21
Category : Mathematics
ISBN : 0080462472
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method · Construction of lower and upper solutions in problems · Working applications and illustrated theorems by examples · Description of the history of the method and Bibliographical notes
Author : Bailey
Publisher : Academic Press
Page : 190 pages
File Size : 48,6 Mb
Release : 1968
Category : Computers
ISBN : 9780080955520
Nonlinear Two Point Boundary Value Problems
Author : M.R. Grossinho,M. Ramos,C. Rebelo,L. Sanchez
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201915
This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed. Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including: * periodic solutions of systems with p-Laplacian type operators (J. Mawhin) * bifurcation in variational inequalities (K. Schmitt) * a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega) * asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl) * mechanics on Riemannian manifolds (W. Oliva) * techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets) A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.
Author : Philip Korman
Publisher : World Scientific
Page : 256 pages
File Size : 55,7 Mb
Release : 2012-02-10
Category : Mathematics
ISBN : 9789814458061
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results. Contents:Curves of Solutions on General Domains:Continuation of SolutionsSymmetric Domains in R2Turning Points and the Morse IndexConvex Domains in R2Pohozaev's Identity and Non-Existence of Solutions for Elliptic SystemsProblems at ResonanceCurves of Solutions on Balls:Preliminary ResultsPositivity of Solution to the Linearized ProblemUniqueness of the Solution CurveDirection of a Turn and Exact MultiplicityOn a Class of Concave-Convex EquationsMonotone Separation of GraphsThe Case of Polynomial ƒ(u) in Two DimensionsThe Case When ƒ(0) < 0Symmetry BreakingSpecial EquationsOscillations of the Solution CurveUniqueness for Non-Autonomous ProblemsExact Multiplicity for Non-Autonomous ProblemsNumerical Computation of SolutionsRadial Solutions of Neumann ProblemGlobal Solution Curves for a Class of Elliptic SystemsThe Case of a “Thin” AnnulusA Class of p-Laplace ProblemsTwo Point Boundary Value Problems:Positive Solutions of Autonomous ProblemsDirection of the TurnStability and Instability of SolutionsS-Shaped Solution CurvesComputing the Location and the Direction of BifurcationA Class of Symmetric NonlinearitiesGeneral NonlinearitiesInfinitely Many Curves with Pitchfork BifurcationAn Oscillatory Bifurcation from Zero: A Model ExampleExact Multiplicity for Hamiltonian SystemsClamped Elastic Beam EquationSteady States of Convective EquationsQuasilinear Boundary Value ProblemsThe Time Map for Quasilinear EquationsUniqueness for a p-Laplace Case Readership: Graduate students and researchers in analysis and differential equations, and numerical analysis and computational mathematics. Keywords:Global Solution Curves;Exact MultiplicityKey Features:Integration of theoretical study of exact multiplicity results with numerical analysis and computationIncludes computing bifurcation diagramsPresents several computer-assisted proofs of uniqueness and exact multiplicity theoremsComputations using power series
Author : Herbert B. Keller
Publisher : Unknown
Page : 61 pages
File Size : 54,8 Mb
Release : 1984
Category : Boundary value problems
ISBN : OCLC:283288241
Author : John R Graef,Lingju Kong
Publisher : World Scientific
Page : 292 pages
File Size : 51,5 Mb
Release : 2015-08-26
Category : Mathematics
ISBN : 9789814696562
Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial differential equations as well as for difference equations. In this monograph, we look at how variational methods can be used in all these settings. In our first chapter, we gather the basic notions and fundamental theorems that will be applied in the remainder of this monograph. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with the Sturm-Liouville problems, multi-point boundary value problems, problems with impulses, partial differential equations, and difference equations. An extensive bibliography is also included.
Author : Sanford M. Roberts,Jerome S. Shipman
Publisher : Elsevier Publishing Company
Page : 300 pages
File Size : 49,7 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015013040491
Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 1767 pages
File Size : 53,9 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9781351643917
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
Author : Stuart P. Hastings,J. Bryce McLeod
Publisher : American Mathematical Soc.
Page : 393 pages
File Size : 44,8 Mb
Release : 2011-12-15
Category : Mathematics
ISBN : 9780821846940
This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed. The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years. Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.
Author : A. Canada,P. Drabek,A. Fonda
Publisher : Elsevier
Page : 752 pages
File Size : 55,7 Mb
Release : 2006-08-21
Category : Mathematics
ISBN : 0080463819
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 50,8 Mb
Release : 2011-11-13
Category : Mathematics
ISBN : 9781461405023
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.