| Description |
1 online resource (615 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Authors -- Preface -- 1. Introduction to Stability Methods -- 1.1 Introduction -- 1.2 Preliminaries -- 1.3 A priori estimation method -- 1.3.1 Delay-independent conditions -- 1.3.2 Delay-dependent conditions -- 1.4 Reduction to a system of differential equations -- 1.5 W-transform method -- 1.5.1 Delay-independent conditions -- 1.5.2 Delay-dependent conditions -- 1.6 Remarks and exercises -- 1.6.1 Possible topics for a course of stability FDE -- 1.6.2 Exercises -- 2. Stability: A priori Estimation Method -- 2.1 Introduction |
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2.2 Preliminaries -- 2.3 Estimation of solutions -- 2.3.1 Estimates of x -- 2.3.2 Estimates of x -- 2.3.3 Estimate of x -- 2.4 Exponential stability conditions -- 2.5 Some generalizations -- 2.5.1 Equations with several delays -- 2.5.2 Equation with integral terms -- 2.5.3 Equation with distributed delays -- 2.6 Equations with perturbations by a damping term -- 2.6.1 Estimation of solutions -- 2.6.2 Exponential stability conditions -- 2.7 Neutral differential equations -- 2.7.1 Introduction and preliminaries -- 2.7.2 Explicit stability conditions -- 2.8 Remarks and open problems |
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3. Stability: Reduction to a System of Equations -- 3.1 Introduction -- 3.2 Application of M-matrix -- 3.2.1 Introduction -- 3.2.2 Equations without delay in damping terms -- 3.2.3 Equations with delay in damping terms -- 3.3 1+1/e stability conditions -- 3.3.1 Introduction -- 3.3.2 Main results -- 3.4 Nonlinear equations -- 3.5 Sunflower model and its modifications -- 3.6 Remarks and open problems -- 4. Stability: W-transform Method I -- 4.1 Introduction and preliminaries -- 4.2 Main results -- 4.2.1 Equations without delays in the damping terms |
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4.2.2 Equations with delays in the damping terms -- 4.3 Remarks and some topics for future research -- 5. Stability: W-transform Method II -- 5.1 Introduction -- 5.2 Formulations of main results -- 5.3 Values of integrals of the modulus of Cauchy functions for auxiliary equations -- 5.4 Proofs of main theorems -- 5.5 Comments and open problems -- 6. Exponential Stability for Equations with Positive and Negative Coefficients -- 6.1 Introduction -- 6.2 Positivity of the Cauchy functions and stability -- 6.2.1 Tests of positivity -- 6.2.2 Auxiliary results -- 6.2.3 Main results |
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6.3 Application of W-method -- 6.3.1 Main results -- 6.3.2 Proofs of main theorems -- 6.4 Transformations to equations with a damping term -- 6.4.1 Delay differential equations -- 6.4.2 Integro-differential equations and equations with distributed delays -- 6.4.3 Equation with a damping term -- 6.5 Remarks and open problems -- 7. Connection Between Nonoscillation and Stability -- 7.1 Introduction -- 7.2 Preliminaries -- 7.3 Nonoscillation criteria -- 7.4 Exponential stability of delay differential equations |
| Notes |
Description based upon print version of record |
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7.5 Exponential stability of integro-differential equations and equations with distributed delays |
| Subject |
Functional differential equations.
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Functional differential equations
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| Form |
Electronic book
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| Author |
Berezansky, Leonid
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Koplatadze, Roman
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| ISBN |
9781000048551 |
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1000048551 |
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9781000048636 |
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1000048632 |
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9780429321689 |
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0429321686 |
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