Ordinary Differential Equations - 1st Edition - ISBN: 9780127436500, 9781483270111

Ordinary Differential Equations

1st Edition

1971 NRL—MRC Conference

Editors: Leonard Weiss
eBook ISBN: 9781483270111
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 622
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Description

Ordinary Differential Equations: 1971 NRL–MRC Conference provides information pertinent to the fundamental aspects of ordinary differential equations. This book covers a variety of topics, including geometric and qualitative theory, analytic theory, functional differential equation, dynamical systems, and algebraic theory.

Organized into two parts encompassing 51 chapters, this book begins with an overview of the results on the existence of periodic solutions of a differential equation. This text then describes an index for the isolated invariant sets of a flow on a compact metric space, which contains exactly the information of the Morse index. Other chapters consider the studies of certain classes of equations that can be interpreted as models of biological or economic processes. This book discusses as well the absolute stability of some classes of integro-differential systems. The final chapter deals with first-order differential equations.

This book is a valuable resource for mathematicians, graduate students, and research workers.

Table of Contents


Participants

Preface

I. Invited Papers

A General Approach to Linear Problems for Nonlinear Ordinary Differential Equations

Differential Relations

Conditions for Boundedness of Systems of Ordinary Differential Equations

On a Generalization of the Morse Index

Equations Modelling Population Growth, Economic Growth, and Gonorrhea Epidemiology

Absolute Stability of Some Integro-Differential Systems

A New Technique for Proving the Existence of Analytic Functions

Potentials with Closed Trajectories on Surfaces of Revolution

Local Behavior of Autonomous Neutral Functional Differential Equations

External Properties of Biconvex Contingent Equations

Asymptotic Distribution of Eigenvalues

On Logarithmic Derivatives of Solutions of Disconjugate Linear nth Order Differential Equations

Uniqueness and Existence of Solutions of Boundary Value Problems for Ordinary Differential Equations

Realization of Continuous-Time Linear Dynamical Systems: Rigorous Theory in the Style of Schwartz

Dissipative Systems

Relaxation Oscillations and Turbulence

Geometric Differential Equations

Tauberian Theorems and Functional Equations

Perturbations of Volterra Equations

Involutory Matrix Differential Equations

Control Theory of Hyperbolic Equations Related to Certain Questions in Harmonic Analysis and Spectral Theory (An Outline)

The Homology of Invariant Sets of Flows

Linear Differential Equations with Delays: Admissibility and Exponential Dichotomies

Topological Dynamical Techniques for Differential and Integral Equations

Double Asymptotic Expansions for Linear Ordinary Differential Equations

Oscillatory Property for Second Order Differential Equations

II. Seminar Papers

A Pictorial Study of an Invariant Torus in Phase Space of Four Dimensions

Autonomous Perturbations of Some Hamiltonian Systems, All of Whose Solutions Are Periodic

Some Boundary Value Problems for Nonlinear Ordinary Differential Equations on Infinite Intervals

Positively Stable Dynamical Systems

A Nonlinear Predator-Prey Problem

Lie Algebras and Linear Differential Equations

An Algorithm for Computing Liapunov Functional for Some Differential-Difference Equations

Periodic Solutions to Hamiltonian Systems with Infinitely Deep Potential Wells

Variational Problems with Delayed Argument

Frequency-Domain Criteria for Dissipativity

Note on Analytic Solutions of Nonlinear Ordinary Differential Equations at an Irregular Type Singularity

Stability of Compactness for Functional Differential Equations

Kronecker Invariants and Feedback

Lower Bounds and Uniqueness for Solutions of Evolution Inequalities in a Hubert Space

Remarks on Linear Differential Equations with Distributional Perturbations

Computing Bounds for Focal Points and for σ-Points for Second-Order

Linear Differential Equations

Global Controllability of Nonlinear Systems

The Phragmén-Lindelöf Principle and a Class of Functional Differential Equations

Singular Perturbations and the Linear State Regulator Problem

Delay-Feedback, Time-Optimal, Linear Time-Invariant Control Systems

The Family of Direct Periodic Orbits of the First Kind in the Restricted Problem of Three Bodies

A General Theory of Liapunov Stability

Finite Time Stability of Linear Differential Equations

Second Order Oscillation with Retarded Arguments

A Note on Malmquist's Theorem on First-Order Differential Equations

Details

No. of pages:
622
Language:
English
Copyright:
© Academic Press 1972
Published:
Imprint:
Academic Press
eBook ISBN:
9781483270111

About the Editor

Leonard Weiss