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040 _aOCoLC-P
_beng
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_cOCoLC-P
020 _a9780429321689
_qelectronic book
020 _a0429321686
_qelectronic book
020 _a9781000048636
_qelectronic book
020 _a1000048632
_qelectronic book
020 _a9781000048551
_qelectronic book
020 _a1000048551
_qelectronic book
020 _z9780367337544
035 _a(OCoLC)1155637988
035 _a(OCoLC-P)1155637988
050 4 _aQA372
_b.B47 2020
072 7 _aMAT
_x007000
_2bisacsh
072 7 _aMAT
_x040000
_2bisacsh
072 7 _aMAT
_x037000
_2bisacsh
072 7 _aPBK
_2bicssc
082 0 4 _a515/.35
_223
100 1 _aBerezansky, Leonid,
_eauthor.
245 1 0 _aOscillation, nonoscillation, stability and asymptotic properties for second and higher order functional differential equations /
_cLeonid Berezansky, Alexander Domoshnitsky, Roman Koplatadze.
264 1 _aBoca Raton :
_bCRC Press,
_c[2020]
300 _a1 online resource (xxiv, 590 pages).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
500 _a"A Chapman & Hall book" -- Title Page.
505 8 _aBiographyPrefaceIntroduction 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.
520 _aAsymptotic 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.
588 _aOCLC-licensed vendor bibliographic record.
650 7 _aMATHEMATICS / Differential Equations
_2bisacsh
650 7 _aMATHEMATICS / Functional Analysis
_2bisacsh
650 0 _aFunctional differential equations.
650 0 _aStability.
700 1 _aDomoshnitsky, Alexander,
_eauthor.
700 1 _aKoplatadze, Roman,
_eauthor.
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429321689
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999 _c127377
_d127377