Bifurcation theory and nonlinear eigenvalue problems, 1967 by Joseph Bishop Keller

Cover of: Bifurcation theory and nonlinear eigenvalue problems, 1967 | Joseph Bishop Keller

Published by Courant Institute of Mathematical Sciences in [New York .

Written in English

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  • Nonlinear theories.,
  • Differential equations, Nonlinear.,
  • Mathematical physics.,
  • Bifurcation theory.

Edition Notes

Book details

Statementedited by Joseph B. Keller and Stuart Antman.
ContributionsAntman, S. S. joint author., Courant Institute of Mathematical Sciences.
LC ClassificationsQA427 .K4
The Physical Object
Paginationv, 346 p.
Number of Pages346
ID Numbers
Open LibraryOL5600250M
LC Control Number68006558

Download Bifurcation theory and nonlinear eigenvalue problems, 1967

"Based upon a series of 15 lectures presented to the Seminar on bifurcation theory and nonlinear eigenvalue problems held at the Courant Institute during " Description: v, pages illustrations 28 cm. OCLC Number: Notes: Ce volume est basé sur le"Seminar on bifurcation theory and nonlinear eigenvalue problems"qui s'est tenu en au "Courant Institute of Mathematical Sciences" de l'Université de New York " -- cf.

préface. Yihong Du, in Handbook of Differential Equations: Stationary Partial Differential Equations, 1 Introduction.

Bifurcation theory provides a bridge between the linear world and the more complicated nonlinear world, and thus plays an important role in the study of various nonlinear problems. Nonlinear elliptic boundary value problems enjoy many nice properties that allow the use of a.

Something more the reader will find about problems of type K, for which I have focused on a short account of some basic results and methods from Bifurcation Theory on the one hand (Section ), and to a brief description of a very special—maybe the “closest to linear”—nonlinear eigenvalue problem on the other (Section ).Cited by: 4.

In this paper we consider global bifurcation of solutions of nonlinear eigenvalue problems for second order uniformly elliptic equations with an indefinite weight function and the Dirichlet Author: Hansjörg Kielhöfer. The deep connection between bifurcation points and the spectrum of linear operators involved in problems is pointed out.

The presentation consists of two parts regarding the used approach: degree theory and implicit function theorem. This chapter describes a global theorem for nonlinear eigenvalue problems and applications. Equations of the form () occur in many parts of mathematical physics, particularly in fluid dynamics and in elasticity theory.

Thus, the nature of the structure Bifurcation theory and nonlinear eigenvalue problems the set of their solution is an important by: Bounds for nonlinear eigenvalue problems Article (PDF Available) in Electronic Journal of Differential Equations Conference(06) January with 22 Reads How we measure 'reads'.

Crandall M.G., Rabinowitz P.H. () Mathematical Theory of Bifurcation. In: Bardos C., Bessis D. (eds) Bifurcation Phenomena in Mathematical Physics and Related Topics. NATO Advanced Study Institutes Series (Series C — Mathematical and Physical Sciences), vol Cited by: Bifurcation Theory and Nonlinear Eigenvalue Problems, Keller, Joseph B., Antman, Stuart Published by Courant Institute of Mathematical Sciences ().

Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is 1967 book not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, physicists and economists.

References on Bifurcation Theory Nobuhiko Otoba August 6, Pergamon Press Book, The Macmillan Co., New York, MR [42] Paul H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J.

Functional Analysis 7 (), { MR A dynamical system is a manifold M called the phase (or state) space endowed with a family of smooth evolution functions Φ t that for any element of t ∈ T, the time, map a point of the phase space back into the phase space.

The notion of smoothness changes with applications and the type of manifold. There are several choices for the set T is taken to be the reals, the dynamical. Semilinear parabolic problems are considered for which we prove their topological sensitivity to arbitrarily small perturbations of the nonlinear term.

This instability result is a consequence of the sensitivity of the multiplicity of solutions of the corresponding nonlinear elliptic : Mickaël D. Chekroun. Unilateral global interval bifurcation for Kirchhoff type problems and its applications.

Eigenvalue problems for the $ p $-Laplacian, Nonlinear Analysis: Theory, Methods & Applications, 64 (),Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc., 71 ( Cited by: 1. We consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion precesses.

When the reaction term has a particular form, f(u) =u3, the problem has a unique positive solution that satisfies a conserved integral condition.

by R. Cook on “nonlinear eigenvalue problems" reviews the status on continuation methods and bifurcation algorithms. Zangwill, W. & C. Garcia, Pathways to solutions, fixed points, and equilibria, Prentice-Hall (). - A text on continuation schemes with a. The numerical solution of nonlinear problems, Clarendon Press ().

Part I of this work contains 6 articles on nonlinear algebraic equations. The article by R. Cook on finonlinear eigenvalue problems" reviews the status on continuation methods and bifurcation algorithms.

Bifurcation problems for nonlinearly elastic structures, in Rabinowitz Nonlinear eigenvalue problems for the whirling of heavy elastic strings.

Nonlinear Problems of Elasticity (book in preparation). ANTMAN, S. and E. CARBONE, Shear and. From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations.

Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Tămăşan, On the bifurcation of the null solution of some mildly nonlinear elliptic boundary value problems, An.

Univ. Ovidius Constanta, Seria Matematica, 5. () Estimation of the bifurcation coefficient for nonlinear eigenvalue problems. Zeitschrift für angewandte Mathematik und Physik ZAMP() Lower Bounds for Stekloff and Free Membrane by:   The present study focuses on the development of nonlinear interval finite elements (NIFEM) for beam and frame problems.

Three constitutive models have been used in the present study, viz., bilinear, Ramberg–Osgood, and cubic models, to illustrate the development of by: 4.

Nonlinear Functional Analysis by Klaus Deimling. Paperback Exercises.- § Further Topics in Bifurcation Theory.- Variational Methods.- Stability.- Hopf Bifurcation and Last Remarks.- In the second half of the twentieth century many prominent, ex­ emplary problems in nonlinear analysis were View Product [ x Author: Klaus Deimling.

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non Cited by: () Estimation of the bifurcation coefficient for nonlinear eigenvalue problems.

Zeitschrift für angewandte Mathematik und Physik ZAMPJ. Kuttler and V. by: A POD reduced-order model for eigenvalue problems with application to reactor physics. International Journal for Numerical Methods in Engineering, Vol.

95, Issue. 12, p. International Journal for Numerical Methods in Engineering, Vol. 95, Issue. 12, p. Author: Philip Holmes, John L. Lumley, Gahl Berkooz, Clarence W. Rowley. Exterior boundary value problems for perturbed equations of elliptic type.- Linear transport theory and an indefinite Sturm-Liouville problem.- Non-normalizable eigenfunction expansions for ordinary differential operators.- Some aspects and recent developments in linear control theory.- Eigenvalue problems and the Riemann zeta-function problems for ordinary differential equations 31 Chapter IV.

Existence theorems for equations in normed spaces 42 Chapter V. Boundary value problems for second order nonlinear vector differential equations 51 Chapter VI.

Periodic solutions of ordinary differential equations with. Kratochvil and J. Necas: Secant modulus method for the construction of a solution of nonlinear eigenvalue problems. Boll. Mat. Ital. B 16 (2), (). Necas: Variational inequalities in elasticity and plasticity with application to Signorini's problems and to flow theory of plasticity.

Angew. Math. Mech. 60 (6), The general theory of elastic stability invented by Koiter (, “On the Stability of Elastic Equilibrium,” Ph.D. thesis, Delft, Holland) motivated the development of a series of asymptotic approaches to deal with the initial postbuckling behavior of structures.

These approaches, which played a pivotal role in the precomputer age, are somewhat overshadowed by the progress of computational Cited by: 4. AbstractThe nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker ’s theory and Polach model including dead-zone clearance.

This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail Cited by: 1.

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Spectral and Dynamical Stability of Nonlinear Waves (Applied Mathematical Sciences Book ) - Kindle edition by Kapitula, Todd, Promislow, Keith. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading Spectral and Dynamical Stability of Nonlinear Waves (Applied Mathematical Sciences Book ).5/5(1). I tried to select only the works in book formats, "real" books that are mainly in PDF format, so many well-known html-based mathematics web pages and online tutorials are left out.

Click here if you prefer a categorized directory of mathematics books. Shareable Link. Use the link below to share a full-text version of this article with your friends and colleagues.

Learn more. Dynamical Systems, Nonlinear Waves. We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general May 7, Center manifold reduction is a standard technique in bifurcation theory, reducing the.

American Mathematical Society Charles Street Providence, Rhode Island or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S.

Patent and Trademark. The sizes of the matrices vary from very small, such as counter example matrices, to very large. One drawback of the collection is that it contains few non-Hermitian eigenvalue problems.

Many of the eigenvalue problems in the collection are from structural engineering, which are. This paper traces the advances made in the exploitation of group theory in areas such as bifurcation analysis, vibration analysis and finite-element analysis, and outlines the various schemes of implementation currently available.

International Journal for Nonlinear Mechanics, 31 (1),Healey T.J., Treacy J.A., "Exact block Cited by: 9. Nonlinear Theory and Its Applications, IEICE 2, ().

Free Vibrations of Trusses by Fourier Decomposition, and Homotopy Methods for Nonlinear Matrix Eigenvalue Problems, I and II. J. Math. Anal. Appl.() and().

Enclosures for Two-Point Boundary Value Problems near Bifurcation Points. In.Bifurcation and nonlinear eigenvalue problems C. Bardos, J. M. Lasry, M.

Schatzman Bifurcation theory and applications L. Salvadori Bifurcation Theory: An Introduction With .Full text of "Introduction to applied nonlinear dynamical systems and chaos" See other formats.

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