عنوان
پدید آورنده
موضوع
رده
QA614.8
QA614
.
8
کتابخانه
محل استقرار
303015419X
3030154203
3030154211
303015422X
9783030154196
9783030154202
9783030154219
9783030154226
9783030154196
Functional dynamic equations on time scales /
[Book]
Svetlin G. Georgiev.
Cham :
Springer,
2019.
1 online resource
Intro; 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
2.3.7 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
4.4 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
6.4 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
8.4 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
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This 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.
Springer Nature
com.springer.onix.9783030154202
9783030154196
9783030154219
9783030154226
Difference equations.
Differentiable dynamical systems.
Difference equations.
Differentiable dynamical systems.
MATHEMATICS-- Topology.
MAT-- 038000
PBKF
PBKF
514/
.
74
23
QA614
.
8
Georgiev, Svetlin
20200823084452.0
pn
مطالعه متن کتاب [Book]
Y
