rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Oscillation, nonoscillation, stability and asymptotic properties for second and higher order functional differential equations
  title info:
    title: MATHnetBASE
  name:
    name part: Berezansky, Leonid
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Domoshnitsky, Alexander
    role:
      role term: author.
  name:
    name part: Koplatadze, Roman
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2020
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xxiv, 590 pages).
  abstract: Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The control in the mechanical processes leads to mathematical models with second order delay differential equations. Stability and stabilization of second order delay equations are one of the main goals of this book. The book is based on the authors' results in the last decade. Features: Stability, oscillatory and asymptotic properties of solutions are studied in correlation with each other. The first systematic description of stability methods based on the Bohl-Perron theorem. Simple and explicit exponential stability tests. In this book, various types of functional differential equations are considered: second and higher orders delay differential equations with measurable coefficients and delays, integro-differential equations, neutral equations, and operator equations. Oscillation/nonoscillation, existence of unbounded solutions, instability, special asymptotic behavior, positivity, exponential stability and stabilization of functional differential equations are studied. New methods for the study of exponential stability are proposed. Noted among them inlcude the W-transform (right regularization), a priory estimation of solutions, maximum principles, differential and integral inequalities, matrix inequality method, and reduction to a system of equations. The book can be used by applied mathematicians and as a basis for a course on stability of functional differential equations for graduate students.
  table of contents: BiographyPrefaceIntroduction to Stability Methods. Stability: A priori Estimation Method. Stability: Reduction to a System of Equations. Stability: W-transform Method I. Stability: W-transform Method II. Exponential Stability for Equations with Positive and Negative Coeffcients. Connection Between Nonoscillation and Stability. Stabilization for Second Order Delay Models, Simple Delay Control.Stabilization by Delay Distributed Feedback Control. Wronskian of Neutral FDE and Sturm Separation Theorem. Vallee-Poussin Theorem for Delay and Neutral DE. Sturm Theorems and Distance between Adjacent Zeros. Unbounded Solutions and Instability of Second Order DDE. Upper and Lower Estimates of Distances Between Zeros and Floquet Theory for Second Order DDE. Distribution of Zeros and Unboundedness of Solutions to Partial DDE. Second Order Equations: Oscillation and Boundary Value Problems. Stability of Third Order DDE. Operator Differential Equations. Properties A and B of Equations with a Linear Minorant. On Kneser-Type Solutions. Monotonically Increasing Solutions. Specific Properties of FDE. A Useful Theorems from Analysis. B Functional-differential Equations. Bibliography. Index.
  target audience: adult
  note: Leonid Berezansky, Alexander Domoshnitsky, Roman Koplatadze.
  note: "A Chapman & Hall book" -- Title Page.
  subject:
    topic: MATHEMATICS / Differential Equations
  subject:
    topic: MATHEMATICS / Functional Analysis
  subject:
    topic: Functional differential equations
  subject:
    topic: Stability
  classification: QA372 .B47 2020
  classification: 515/.35
  identifier: 9780429321689
  identifier: 0429321686
  identifier: 9781000048636
  identifier: 1000048632
  identifier: 9781000048551
  identifier: 1000048551
  identifier: 9780367337544
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCoLC-P
    record creation date: 200528
    record change date: 20220613180032.7
    record identifier: in00004581956
    language of cataloging:
      language term: eng