Dynamical Systems

Dynamical Systems: An International Symposium, Volume 1 contains the proceedings of the International Symposium on Dynamical Systemsheld at Brown University in Providence, Rhode Island, on August 12-16, 1974. The symposium provided a forum for reviewing the theory of dynamical systems in relation to ordinary and functional differential equations, as well as the influence of this approach and the techniques of ordinary differential equations on research concerning certain types of partial differential equations and evolutionary equations in general.

Comprised of 29 chapters, this volume begins with an introduction to some aspects of the qualitative theory of differential equations, followed by a discussion on the Lefschetz fixed-point formula. Nonlinear oscillations in the frame of alternative methods are then examined, along with topology and nonlinear boundary value problems. Subsequent chapters focus on bifurcation theory; evolution governed by accretive operators; topological dynamics and its relation to integral equations and non-autonomous systems; and non-controllability of linear time-invariant systems using multiple one-dimensional linear delay feedbacks. The book concludes with a description of sufficient conditions for a relaxed optimal control problem.

This monograph will be of interest to students and practitioners in the field of applied mathematics.

List of Contributors

Preface

Memorial Address

Contents of Volume 2

Chapter 1 Qualitative Theory

Some Aspects of the Qualitative Theory of Differential Equations

The Lefschetz Fixed-Point Formula; Smoothness and Stability

Chapter 2 General Theory

Nonlinear Oscillations in the Frame of Alternative Methods

Topology and Nonlinear Boundary Value Problems

A Survey of Bifurcation Theory

Generalized Linear Differential Systems and Associated Boundary Problems

Some Stochastic Systems Depending on Small Parameters

Bifurcation

Chapter 3 Evolutionary Equations

An Introduction to Evolution Governed by Accretive Operators

Evolution Equations in Infinite Dimensions

Chapter 4 Functional Differential Equations

Functional Differential Equations of Neutral Type

Functional Differential Equations—Generic Theory

Chapter 5 Topological Dynamical Systems

Stability Theory and Invariance Principles

Topological Dynamics and Its Relation to Integral Equations and Nonautonomous Systems

Chapter 6 Partial Differential Equations

Nonlinear Oscillations under Hyperbolic Systems

Liapunov Methods for a One-Dimensional Parabolic Partial Differential Equation

Discontinuous Periodic Solutions of an Autonomous Wave Equation

Continuous Dependence of Forced Oscillations for ut = ∇ ⋅ γ(|∇u|)∇u

Partial Differential Equations and Nonlinear Hydrodynamic Stability

Chapter 7 Control Theory

On Normal Control Processes

Projection Methods for Hereditary Systems

Lower Bounds for the Extreme Value of a Parabolic Control Problem

Controllability for Neutral Systems of Linear Autonomous Differential-Difference Equations

Local Controllability of a Hyperbolic Partial Differential Equation

A Connection Between Optimal Control and Disconjugacy

Noncontrollability of Linear Time-Invariant Systems Using Multiple One-Dimensional Linear Delay Feedbacks

A Perturbation Method for the Solution of an Optimal Control Problem Involving Bang-Bang Control

Sufficient Conditions for a Relaxed Optimal Control Problem

Author Index

Subject Index