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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
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
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
- No. of pages:
- © Academic Press 1976
- 1st January 1976
- Academic Press
- eBook ISBN:
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