# International Conference on Differential Equations

## 1st Edition

**Editors:**H.A. Antosiewicz

**eBook ISBN:**9781483259130

**Imprint:**Academic Press

**Published Date:**1st January 1975

**Page Count:**856

## Description

International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods).

Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory.

This monograph will be of interest to students and instructors of mathematics.

## Table of Contents

Invited Addresses and Research Reports

Contributed Papers

Preface

Invited Addresses and Research Reports

Continuous Extensions: Their Construction and Their Application in the Theory of Differential Equations

Boundary Control of the Diffusion Equation: A Semigroup Theoretical Approach

An Abstract Framework for Approximate Solutions to Optimal Control Problems Governed by Hereditary Systems

Lower Closure and Existence Theorems in Optimal Control

A Singular Cauchy Problem and Generalized Translations

Some Models for Population Growth with Harvesting

The Problem of Hill for Systems

Alternative Methods in Nonlinear Analysis

Minimum Principles and Positive Solutions for a Class of Nonlinear Diffusion Problems

Diagonalization Method in Singular Perturbations

Eigenfunction Expansions for Selfadjoint Subspaces Generated by Symmetric Ordinary Differential Operators

A Nonlinear Oscillation Theorem

On Global Controllability

Matrices of Rational Functions

Suppression of Oscillations in Nonlinear Systems

Duality of Various Notions of Controllability and Observability

A Case History in Singular Perturbations

On the Strong Limit-Point Condition of Second Order Differential Expressions

A Nonlinear Parabolic Partial Differential Equation in Population Genetics

Fixed Points and Uniqueness

Periodic Solutions of Perturbed Lotka-Volterra Systems

Continuous Dependence on a Parameter for Ordinary and Functional Differential Equations

The Solution Operator with Infinite Delays

Brouwer Fixed Point Theorem versus Contraction Mapping Theorem in Optimal Control Theory

Recent Results in the Asymptotic Integration of Linear Differential Systems

Integration of Linear Differential Equations by Laplace-Stieltjes Transforms

Solutions Near Bifurcated Steady States

Recent Advances in the Analytic Theory of Nonlinear Differential Equations with an Irregular Type Singularity

Nagumo Conditions for Ordinary Differential Equations

Periodic Solutions of Ordinary Differential Equations as Fixed Points of the Translation Mapping Near Certain Critical Cases

Toward a Unification of Ordinary Differential Equations with Nonlinear Semi-Group Theory

Degeneracy of Functional Differential Equations

A Liapunov Inequality for Nonlinear Systems

Existence and Comparison Results of Differential Equations in a Banach Space

Adiabatic Invariants for Linear Hamiltonian Systems

Limits of Solutions of Integrodifferential Equations

On the Summation of Formal Solutions at an Irregular Singular Point by Factorial Series

Invariant Sets for Evolution Systems

Recent Results on Periodic Solutions of Differential Equations

Factorization of Fredholm Operators on Analytic Functions

Some Fundamental Theory of Volterra Integral Equations

On the Global Behavior of a Nonlinear Volterra Equation

The Singular Perturbation Approach to Singular Arcs

Existence Theory in Optimal Control Problems: The Underlying Ideas

Recent Error Analysis of Asymptotic Solutions of Linear Differential Equations

Accessible Sets in Control Theory

A Class of Optimal Control Problems Involving Higher Order Isotonic Approximation

A Singular Point Problem Arising in Control Theory

A Spectral Theory for Linear Almost Periodic Differential Equations

Subdominant Solutions Admitting a Prescribed Stokes Phenomenon

Necessary Conditions without Differentiability in Unilateral and Minimum Control Problems

Some Recent Results in the Theory of Adiabatic Invariants

The Role of Positive Definite Functions in the Study of Volterra Integral Equations

Favard's Conditions in Linear Almost Periodic Systems

Contributed Papers

Stability of Non-Compact Sets

A Generalized Fuchsian Theory and Some Applications

Differential Equations without Linear Terms

A Note on the Existence of Periodic Solutions of x"(t)+f(t,x(t)) = 0

Geometric Views in Existence Theory

Point wise Degeneracy of Linear Time-Invariant Delay Differential Systems with Distributed Lag

Asymptotic Equivalence of an Ordinary and a Functional Differential Equation

Starting in Maximum Polynomial Degree Nordsieck Gear Methods

A Criterion for the Uniform Asymptotic Stability of a Class of Differential-Difference Equations

Nonoscillation and Integral Inequalities

Equivalence Classes of Functionals and Solvability of Optimal Control Problems

From "Multiple Balayage" to Fuzzy Sets

Contrast Enhancement, Short Term Memory and Attention in Reverberating Neural Networks

Asymptotic Stability in Systems with Several Parameters Multiplying the Derivatives

Applications of an Alternative Theorem for Singular Differential Systems

On Approximate and True Solutions of a Nonlinear Singular Perturbation Problem

On the Variation of the Solutions of a Nonlinear Integral Equation

Oscillation Criteria for a Fourth Order Self-Adjoint Linear Differential Equation

Complex Functional Equations Whose Solutions Have Natural Boundaries

Unbounded Invariant Curves for Flows in Three Dimensional Space

Limit Solutions of (E)x" + g(x) = kf(x, x')x' = εp(t), k, ε Small

Stability of Underdetermined Systems

On Controlling Shocks in Solutions of Nonlinear Partial Differential Equations

Asymptotic Solutions and Stokes Phenomenon for a Certain Ordinary Differential Equation

Theory of Partial Stability and Partial Boundedness of Functional Differential Equations

The Singularly Perturbed Initial-Value Problem When the Reduced Path Encounters a Point of Bifurcation

Natural Caratheodory Conditions for Linear Retarded Equations

Differential Equations of Advanced Type

## Details

- No. of pages:
- 856

- Language:
- English

- Copyright:
- © Academic Press 1975

- Published:
- 1st January 1975

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483259130