International Conference on Differential Equations

International Conference on Differential Equations

1st Edition - January 1, 1975

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  • Editor: H.A. Antosiewicz
  • eBook ISBN: 9781483259130

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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


    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

Product details

  • No. of pages: 856
  • Language: English
  • Copyright: © Academic Press 1975
  • Published: January 1, 1975
  • Imprint: Academic Press
  • eBook ISBN: 9781483259130

About the Editor

H.A. Antosiewicz

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