Qualitative Theory of Volterra Difference Equations. (2018)

• Record Type: Book
• Further Information: Note: Youssef N. Raffoul.
• Authors: Raffoul, Youssef N
• Contents: Intro; Preface; Contents; 1 Stability and Boundedness; 1.1 Introduction; 1.2 Introduction to Lyapunov Functions; 1.3 Total Stability via Resolvent; 1.3.1 Application to Perturbed Volterra Difference Equations; 1.4 Uniform Asymptotic Stability via Resolvent; 1.4.1 Application to Scalar Equations; 1.4.2 Homogenous Volterra Equations; (g(n, x)=0); 1.5 Open Problems; 2 Functional Difference Equations; 2.1 Uniform Boundedness and Uniform Ultimate Boundedness; 2.2 Functional Delay Difference Equations; 2.2.1 Application to Volterra Difference Equations; 2.3 Necessary and Sufficient Conditions 2.4 More on Boundedness2.5 Applications to Nonlinear Volterra Difference Equations; 2.6 Open Problems; 3 Fixed Point Theory in Stability and Boundedness; 3.1 Motivation; 3.2 Metrics and Banach Spaces; 3.3 Highly Nonlinear Delay Equations; 3.4 Multiple and Functional Delays; 3.5 Neutral Volterra Equations; 3.6 Almost-Linear Volterra Equations; 3.6.1 Application to Nonlinear Volterra Difference Equations; 3.7 Lyapunov Functionals or Fixed Points; 3.8 Delay Functional Difference Equations; 3.9 Volterra Summation Equations; 3.10 The Need for Large Contraction; 3.11 Open Problems 4 Periodic Solutions4.1 Periodic Solutions in Finite and Infinite Delays Equations; 4.2 Application to Functional Difference Equations; 4.2.1 Finite Delay Difference Equations; 4.2.2 Infinite Delay Volterra Difference Systems; 4.3 Periodicity in Scalar Nonlinear Neutral Systems; 4.4 Periodicity in Vector Neutral Nonlinear Functional Difference Equations; 4.5 Periodicity in Nonlinear Systems with Infinite Delay; 4.5.1 Application to Infinite Delay Volterra Equations; 4.6 Functional Equations with Constant or Periodically Constant Solutions; 4.6.1 The Finite Delay System 4.6.2 The Infinite Delay System4.6.3 The Finite Delay System Revisited; 4.7 Periodic and Asymptotically Periodic Solutions in Coupled Systems; 4.7.1 Periodicity; 4.7.2 Asymptotic Periodicity; 4.8 Open Problems; 5 Population Dynamics; 5.1 Background; 5.2 Formulation of Predator-Prey Discrete Models; 5.3 Cone Theory and Positive Periodic Solutions; 5.3.1 Applications to Infinite Delay Population Models; 5.4 Permanence of Multi-Species Competition Predation; 5.5 Open Problems; 6 Exponential and lp-Stability in Volterra Equations; 6.1 Exponential Stability; 6.2 Criterion for Instability 6.2.1 Applications and Numerical Evidence6.3 Vector Equation; 6.4 z-Transform and Lyapunov Functionals; 6.5 lp-Stability; 6.6 Discretization Scheme Preserving Stability and Boundedness; 6.7 Semigroup; 6.8 Open Problems; References; Index
• Publisher Details: Cham : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 510; Mathematics; Volterra equations; Differential equations -- Qualitative theory; MATHEMATICS / Essays; MATHEMATICS / Pre-Calculus; MATHEMATICS / Reference; Mathematics -- Applied; Applied mathematics; Functional equations; Genetics_xMathematics; Mathematics -- Mathematical Analysis; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319971902; 3319971905
• Related ISBNs: 9783319971896; 3319971891
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF file page (EBSCO, viewed September 19, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.