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000890226 019__ $$a1103891823$$a1105194319
000890226 020__ $$a9783030154202$$q(electronic book)
000890226 020__ $$a3030154203$$q(electronic book)
000890226 020__ $$z9783030154196
000890226 0247_ $$a10.1007/978-3-030-15420-2$$2doi
000890226 0247_ $$a10.1007/978-3-030-15
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000890226 050_4 $$aQA614.8
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000890226 1001_ $$aGeorgiev, Svetlin,$$eauthor.
000890226 24510 $$aFunctional dynamic equations on time scales /$$cSvetlin G. Georgiev.
000890226 264_1 $$aCham :$$bSpringer,$$c2019.
000890226 300__ $$a1 online resource
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000890226 337__ $$acomputer$$bc$$2rdamedia
000890226 338__ $$aonline resource$$bcr$$2rdacarrier
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000890226 5050_ $$aIntro; Preface; Contents; 1 Calculus on Time Scales; 1.1 Forward and Backward Jump Operators, Graininess Function; 1.2 Differentiation; 1.3 Integration; 1.4 The Exponential Function; 1.5 Hyperbolic and Trigonometric Functions; 1.6 Power Series; 1.7 Advanced Practical Problems; 2 Dynamic Systems; 2.1 Structure of Dynamic Systems on Time Scales; 2.2 Constant Coefficients; 2.3 Examples; 2.3.1 The Logistic Model; 2.3.2 Tumor Growth Models; 2.3.3 The Predator-Prey Model of Lotka-Volterra; 2.3.4 The Ricker Model; 2.3.5 The Beverton-Holt Model; 2.3.6 Competition Models
000890226 5058_ $$a2.3.7 Single Species Population Growth Models2.4 Advanced Practical Problems; 3 Functional Dynamic Equations. Basic Concepts, Existence, and Uniqueness Theorems; 3.1 Classification of Functional Dynamic Equations; 3.2 The Method of Steps; 3.3 The Picard-Lindelöf Theorem; 3.4 Existence and Uniqueness Theorems; 3.5 Continuous Dependence on Initial Data; 3.6 Advanced Practical Problems; 4 Linear Functional Dynamic Equations; 4.1 Some Properties of Linear Functional Dynamic Equations; 4.2 First-Order Linear Functional Dynamic Equations; 4.3 Second-Order Linear Functional Dynamic Equations
000890226 5058_ $$a4.4 Advanced Practical Problems5 Stability for First-Order Functional Dynamic Equations; 5.1 Uniform Stability; 5.2 Uniformly Asymptotical Stability; 5.3 Global Stability; 5.4 Asymptotic Stability; 5.5 Exponential Stability I; 5.6 Exponential Stability II; 5.7 Advanced Practical Problems; 6 Oscillations of First-Order Functional Dynamic Equations; 6.1 Positive Solutions; 6.2 Iterated Oscillation Criteria for First-Order Functional Dynamic Equations; 6.3 Oscillations of the Solutions of First-Order Functional Dynamic Equations with Several Delays
000890226 5058_ $$a6.4 Nonoscillations of First-Order Functional Dynamic Equations with Several Delays6.5 Advanced Practical Problems; 7 Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay; 7.1 Reduction to First-Order Linear Functional Dynamic Equations; 7.2 An Oscillation Criteria; 7.3 The Riccati Transformation Technique; 7.4 The Kamenev-Type Oscillation Criteria; 7.5 Advanced Practical Problems; 8 Nonoscillations of Second-Order Functional Dynamic Equations with Several Delays; 8.1 Representation of the Solutions; 8.2 A Nonoscillation Criteria; 8.3 Comparison Theorems
000890226 5058_ $$a8.4 Explicit Nonoscillation and Oscillation Results8.5 Positive Solutions; 8.6 Advanced Practical Problems; 9 Oscillations of Second-Order Nonlinear Functional Dynamic Equations; 9.1 Oscillation Equivalence of a Class of Second-Order Nonlinear Delay Dynamic Equations and a Class of Second-Order Nonlinear Dynamic Equations; 9.2 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations I; 9.3 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations II; 9.4 Oscillation Criteria for a Class Second-Order Half-Linear Delay Dynamic Equations
000890226 506__ $$aAccess limited to authorized users.
000890226 520__ $$aThis book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.
000890226 588__ $$aOnline resource; title from PDF title page (viewed May 7, 2019)
000890226 650_0 $$aDifferentiable dynamical systems.
000890226 650_0 $$aDifference equations.
000890226 77608 $$iPrint version: $$z9783030154196
000890226 852__ $$bebk
000890226 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-15420-2$$zOnline Access$$91397441.1
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000890226 980__ $$aBIB
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