Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

ISBN-13: 9780367337544 / Angielski / Twarda / 2020 / 590 str.

Alexander Domoshnitsky; Leonid Berezansky; Roman Koplatadz

Opis

This book is devoted to oscillation/nonoscillation, exponential stability, instability, existence of solutions with specific asymptotic properties for the second and the higher order functional differential equations (FDEs). These equations include delay differential equations (DDEs), integro-differential equations (IDEs).

Spis treści

Biography
Preface
Introduction 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.