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Sunday, August 16, 2020 | History

1 edition of Global Analysis in Linear Differential Equations found in the catalog.

Global Analysis in Linear Differential Equations

by Mitsuhiko Kohno

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Published by Springer Netherlands in Dordrecht .
Written in English

    Subjects:
  • Differential Equations,
  • Functional equations,
  • Data processing,
  • Algebra,
  • Mathematics,
  • Functions, special

  • About the Edition

    This book treats several topics on the global analysis of linear differential equations in the complex domain, using original methods of analysis developed by K. Okubo and the present author. For example, global analysis of linear differential equations is closely related to that of linear difference equations. Through the asymptotic behaviour of solutions of linear difference equations, connection problems for hypergeometric systems can be solved, i.e. Fuchsian differential equations and Stokes phenomenon for Birkhoff systems. Furthermore, the calculation of monodromy groups is explained in detail. Audience: This volume will be of interest to researchers and graduate students whose work involves ordinary differential equations, special functions, finite difference, functional equations, approximations and expansions, and symbolic/algebraic manipulation.

    Edition Notes

    Statementby Mitsuhiko Kohno
    SeriesMathematics and Its Applications -- 471, Mathematics and Its Applications -- 471
    Classifications
    LC ClassificationsQA372
    The Physical Object
    Format[electronic resource] /
    Pagination1 online resource (xvi, 528 p.)
    Number of Pages528
    ID Numbers
    Open LibraryOL27041422M
    ISBN 109401059462, 9401146055
    ISBN 109789401059466, 9789401146050
    OCLC/WorldCa851368561

    solution of dense linear systems as described in standard texts such as [7], [],or[]. Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a finite-dimensional setting, we have selected for coverage mostlyalgorithms and methods of analysis whichFile Size: KB. Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software.

      In the study of the Cauchy problem for nonlinear wave equations with small initial data, the case where the nonlinearity has the critical power is of special interest. In this case, depending on the structure of the nonlinearity, one may observe global existence and finite time blow-up of solutions.   The Convenient Setting of Global Analysis by Andreas Harmonic Analysis and Partial Differential Equations by Björn E.J One-Parameter Semigroups for Author: Kevin de Asis.

    Global Bifurcation for Fourth-Order Differential Equations with Periodic Boundary-Value Conditions Article (PDF Available) in Mathematical Notes () July with 26 Reads. 11 Differential Equation Theory Existence and uniqueness of solutions Linear systems of differential equations Stiff differential equations 12 Further Evolutionary Problems Many-body gravitational problems Delay problems and discontinuous solutions Problems evolving on a sphere


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Global Analysis in Linear Differential Equations by Mitsuhiko Kohno Download PDF EPUB FB2

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Stokes and B. Riemann inthe Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical.

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann inthe Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering.

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Nonlinear Dispersive Equations: Local and Global Analysis Tao certainly succeeds in writing a vivid and instructional text on nonlinear dispersive Global Analysis in Linear Differential Equations book differential equations. It touches on topics of recent research interest and is a valuable source both for the beginning graduate student and, to some extent, for the advanced researcher.

This book treats several topics on the global analysis of linear differential equations in the complex domain, using original methods of analysis developed by K. Okubo and the present author.

For example, global analysis of linear differential equations is closely related to that of linear difference equations.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation.

This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations.4/5(1). KdV equation, namely the Benjamin-Ono equation, which requires more nonlinear techniques, such as gauge transforms, in order to obtain a satisfactory existence and wellposedness theory.

In the fifth chapter we return to the semilinear equations (NLS and NLW), and now establish large data global existence for these equations in the defocusing. Global Analysis Functional Analysis Examples c-1 Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions.

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Differential Equations and Linear Algebra 12 February by Gilbert Strang. Hardcover. $ This chapter discusses systems of linear differential equations.

It presents the relation of elements of theory developed for systems to the more familiar case of scalar equations. The theory for scalar linear differential equations is best applied directly to the nth-order scalar equation. Many differential equations arise in a context that.

Cite this chapter as: Kohno M. () Linear Differential Equations. In: Global Analysis in Linear Differential Equations.

Mathematics and Its Applications, vol Cited by: 2. Nonlinear Analysis and Differential Equations An Introduction. This lecture note covers the following topics: Analysis In Banach Spaces, The Method of Lyapunov Schmidt, Degree Theory, Global Solution Theorems, Existence and Uniqueness Theorems, Linear Ordinary Differential Equations, Periodic Solutions, Stability Theory, Invariant Sets, Hopf Bifurcation and Sturm-Liouville Boundary Value.

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3 Second-Order Linear Differential Equations 4 Higher-Order Linear Differential Equations 5 Series Solutions of Second-Order Linear Equations 6 The Laplace Transform 7 Systems of First-Order Linear Equations 8 Numerical Methods 9 Nonlinear Differential Equations and Stability 10 Partial Differential Equations.

The basic results about linear ODEs of higher order are essentially the same as for second order equations, with 2 replaced by \(n\).

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Definition. A function \(\phi(x,y)\) is said to be an integral of the characteristic system if \(\phi(x(t),y(t))=const.\) for each characteristic curve.A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject.

The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which.