Differential-Operator Equations: Ordinary and Partial Differential Equations, 1st Edition (Hardback) book cover

Differential-Operator Equations

Ordinary and Partial Differential Equations, 1st Edition

By Yakov Yakubov, Sasun Yakubov

Chapman and Hall/CRC

576 pages

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Hardback: 9781584881391
pub: 1999-11-24
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Description

The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders.

In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains.

Among this volume's other points of interest are:

  • The Abel basis property of a system of root functions

  • Irregular boundary value problems

  • The theory of hyperbolic equations in Gevrey space

  • The theory of boundary value problems for elliptic differential equations with a parameter

  • Table of Contents

    Introduction

    Auxiliary Results

    Completeness and the Abel Basis Property of a System of Root Vectors

    Principally Boundary Value Problems for Ordinary Differential Equations with a Polynomial Parameter

    Principally Regular Elliptic Boundary Value Problems with a Polynomial Parameter

    Elliptic Differential-Operator Equations

    Hyperbolic Differential-Operator Equations

    Parabolic Differential-Operator Equations

    Well-Posed Problems for Partial Differential Equations

    Problems

    Reference Notes

    References

    List of Notations

    Subject Index

    Author Index

    About the Series

    Monographs and Surveys in Pure and Applied Mathematics

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT007000
    MATHEMATICS / Differential Equations
    MAT037000
    MATHEMATICS / Functional Analysis
    SCI040000
    SCIENCE / Mathematical Physics