On ((Lambda))-Nonlinear Boundary Eigenvalue Problems

On ((Lambda))-Nonlinear Boundary Eigenvalue Problems PDF

Author: Christiane Tretter

Publisher: Wiley-VCH

Published: 1993-09

Total Pages: 136

ISBN-13:

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This book discusses nonselfadjoint (Lambda)-nonlinear boundary eigenvalue problems for ordinary differential equations. Asymptotic boundary conditions for uniform convergence of generalized eigenfunction expansions are given by a recursion and expansion theorems are established by a careful analytic study of the asymptotic behaviour of Green's function. The theory is illustrated by various examples from technical mechanics.

A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations

A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations PDF

Author: Paul Waltman

Publisher:

Published: 1970

Total Pages: 20

ISBN-13:

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In this report the authors consider the boundary value problem P sub lambda: x'=f(t, x, y, lambda), y'=g(t, x, y, lambda), A sub 1 y(a)+A sub 2 y'(a)=0, B sub 1 y(b)+B sub 2 y'(b)=0. x(t) and y(t) are scalar functions for t epsilon (a, b), (A sub 1)squared + (A sub 2)squared> zero, (B sub 1)squared +(B sub 2)squared> zero. Values of the parameter lambda (eigenvalues) are sought for which there exists a nontrivial solution of P sub lambda. Two existence theorems are established and these are applied in several situations previously studied. In particular, one theorem applies to a model of a nonlinear vibrating string. (Author).

An Introduction to Nonlinear Boundary Value Problems

An Introduction to Nonlinear Boundary Value Problems PDF

Author: Lakshmikantham

Publisher: Academic Press

Published: 1974-05-31

Total Pages: 399

ISBN-13: 0080956181

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A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

Homotopy Analysis Method in Nonlinear Differential Equations

Homotopy Analysis Method in Nonlinear Differential Equations PDF

Author: Shijun Liao

Publisher: Springer Science & Business Media

Published: 2012-06-22

Total Pages: 566

ISBN-13: 3642251323

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"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

A Class of Nonlinear Eigenvalue Problems

A Class of Nonlinear Eigenvalue Problems PDF

Author: Robert E. L. Turner

Publisher:

Published: 1967

Total Pages: 44

ISBN-13:

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The report considers the nonlinear eigenvalue problem (A - B(lambda))x = 0 in a Hilbert space, where A = or> 0 is compact and B(lambda) is a polynomial with nonnegative operator coefficients, satisfying B(0) = 0. It is shown that if A and B(lambda) are in certain operator classes, then there exists an unconditional basis of the Hilbert space consisting of eigenvectors x corresponding to nonnegative eigenvalues lambda. It is also shown that the nonnegative eigenvalues can be characterized by variational principles. (Author).

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition PDF

Author:

Publisher: ScholarlyEditions

Published: 2012-01-09

Total Pages: 743

ISBN-13: 1464965315

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Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Calculus, Mathematical Analysis, and Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Calculus, Mathematical Analysis, and Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2012 Edition

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2012 Edition PDF

Author:

Publisher: ScholarlyEditions

Published: 2013-01-10

Total Pages: 169

ISBN-13: 1481647636

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Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Numerical Solution of Nonlinear Boundary Value Problems with Applications

Numerical Solution of Nonlinear Boundary Value Problems with Applications PDF

Author: Milan Kubicek

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 338

ISBN-13: 0486463001

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A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

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