Advances in Nonlinear Dynamics

Description

Dedicated to Professor S. Leela in recognition of her significant contribution to the field of nonlinear dynamics and differential equations, this text consists of 38 papers contributed by experts from 15 countries, together with a survey of Professor Leela's work. The first group of papers examines stability, the second process controls, and the third section contains papers on various topics, including solutions for new classes of systems of equations and boundary problems, and proofs of basic theorems. Many of the featured problems are associated with the ideas and methods proposed and developed by Professor Leela. Cover Half Title Series Page Title Page Copyright Page Table of Contents Introduction to the Series Preface 1 A Survey of the Work of S. Leela 2 Oscillatory Property for Second-Order Nonlinear Difference Equations via Lyapunov’s Second Method 3 Asymptotic Behavior of Solutions of Limiting Differential Equations 4 Dissipation and Almost-Periodicity 5 Global Stability in a Hyperbolic Logistic Map with Eventually Fading Memory 6 Exponential Quality of Time-Varying Dynamical Systems: Stability and Tracking 7 Asymptotic Constancy of the Solutions of a Nonlinear Delay Equation 8 A Local Attractor for the Planar System ẋ = y, ẏ = – F(x, y) 9 Stability of Moving Invariant Sets 10 Stability of n-Dimensional Inhomogeneous Delay Differential Equations 11 Uniform Boundedness for Impulsive Systems of Integro-Differential Equations 12 A Contraction Principle 13 Monotone Iterates and Stability for First-Order Ordinary Differential Equations 14 Periodicity and Stability of Semigroups via “λᴷ ∈ ρ (Cᴷ) ⟹ λ ∈ ρ(C )” 15 Asymptotic Stability of Linear Delayed Systems without Instantaneous Dissipative Terms 16 Uniform Stability of a Delay Single Population Model 17 Control in Cardiac Components 18 Control of Nonlinear Delay Differential Economic Systems in W[SUP(1)][SUB(2)] 19 Controllability of Nonlinear Integro-Differential Systems 20 A Second-Order Dubovitskii-Milyutin Theory and Applications to Control 21 The Index for Control Systems 22 Linear Systems Governed by Operators Beyond Hille-Yosida Semigroups 23 Monotone Iterative Methods for Impulsive Hyperbolic Equations 24 Beyond Quenching for Singular Reaction-Diffusion Mixed Boundary-Value Problems 25 Neutral Functional Differential Equations with Abstract Volterra Operators 26 Existence and Multiplicity Results for a Dirichlet Problem with Two Parameters 27 Existence and Uniqueness of Solutions of Impulsive Integro-Differential Equations in Banach Spaces 28 A Nonlocal Multipoint Boundary-Value Problem at Resonance 29 The “Evolution” of Invariance Principles à la Liapunov’s Direct Method 30 First-Order Discontinuous Differential Equations with Functional Boundary Conditions 31 Focal Boundary-Value Problems for Singular Ordinary Differential Equations 32 Some Properties of Differential Equations in the Weak Topology of a Reflexive Banach Space 33 Finite-Dimensional Attractors for von Kármán Systems with Nonlinear Dissipation and Noncompact Nonlinearity 34 Dynamics of Weakly Coupled Parabolic Systems with Nonlocal Boundary Conditions 35 Convex Dependence of Solutions of Dynamic Systems on Time Scales Relative to Initial Data 36 Multipoint Methods for Linear Hamiltonian Systems 37 Global Existence of Solutions to a Class of Nonlinear Systems of Functional Differential Equations 38 Existence Principles for Nonlinear Integral Equations on Semi-Infinite Intervals and Half-Open Intervals 39 Controllability and Observability of Continuous Matrix Liapunov Systems Author Index Subject Index