Nonlinear Systems and Applications

Nonlinear Systems and Applications

An International Conference

1st Edition - January 28, 1977

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  • Editor: V. Lakshmikantham
  • eBook ISBN: 9781483272245

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Nonlinear Systems and Applications: An International Conference contains the proceedings of an International Conference on Nonlinear Systems and Applications held at the University of Texas at Arlington, on July 19-23, 1976. The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability. Various methods used in solving equations are also discussed, including approximation techniques for delay systems. Most of the applications are in the area of the life sciences. Comprised of 59 chapters, this book begins with a discussion on monotonically convergent upper and lower bounds for classes of conflicting populations, followed by an analysis of constrained problems. The reader is then introduced to approximation techniques for delay systems in biological models; differential inequalities for Liapunov functions; and stability or chaos in discrete epidemic models. Subsequent chapters deal with nonlinear boundary value problems for elliptic systems; bounds for solutions of reaction-diffusion equations; monotonicity and measurability; and periodic solutions of some integral equations from the theory of epidemics. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

Table of Contents

  • List of Contributors


    Invited Addresses and Research Reports

    Monotonically Convergent Upper and Lower Bounds for Classes of Conflicting Populations

    A New View on Constrained Problems

    Delay Systems in Biological Models: Approximation Techniques

    Convergence of Volterra Series on Infinite Intervals and Bilinear Approximations

    Differential Inequalities for Liapunov Functions

    Nonlinear Oscillations

    A Comparison Principle for Steady-State Diffusion Operators

    Stability or Chaos in Discrete Epidemic Models

    Analytic Methods for Approximate Solutions of Elliptic Free Boundary Problems

    Nonlinear Boundary Value Problems for Elliptic Systems in the Plane

    Error Propagation and Catastrophes in Protein Synthesizing Machinery

    Some New Applications of Popov's Frequency-Domain Method

    Bounds for Solutions of Reaction-Diffusion Equations

    Imbedding Methods for Bifurcation Problems and Post-Buckling Behavior of Nonlinear Columns

    Monotonicity and Measurability

    Chaotic Behavior in Dynamical Systems

    Stability Technique and Thought Provocative Dynamical Systems

    The Current Status of Abstract Cauchy Problem

    On the Method of Cone-Valued Lyapunov Functions

    Periodic Solutions of Some Integral Equations from the Theory of Epidemics

    Some Recent Progress in Neuro-Muscular Systems

    Applications of the Saturability Technique in the Problem of Stability of Nonlinear Systems

    Nonlinear Evolution Equations and Nonlinear Ergodic Theorems

    On Pure Structure of Dynamic Systems

    Optimizing and Extremizing Nonlinear Boundary Value Problems in Lenticular Antennas in Oceanography, Medicine and Communications: Some Solutions and Some Questions

    A Model for the Statistical Analysis of Cell Radiosensitivity during the Cell Cycle

    Volterra Integral Equations and Nonlinear Semigroups

    Contributed Papers

    The Mathematical Analysis of a Four-Compartment Stochastic Model of Rose Bengal Transport through the Hepatic System

    A More Efficient Algorithm for an Optimal Tour of a Health Care Consumer with Multiple Health Care Facilities in Each County

    Stability of Non-Compact Sets

    Parametric Excitation as the Means of Energy Transfer in Quantal Systems with Reference to Carcinogenesis and Bioenergetics

    Quantum Statistical Foundations for Structural Information Theory and Communication Theory

    Boundary Value Problems for Nonlinear Differential Equations

    Global Solutions for a Problem of Neutron Transport with Temperature Feedback

    Optimal Harvesting for the Logistic and Gompertz Growth Curve

    Maximum and Minimum Degeneracy Set of Linear Time-Invariant Delay-Differential Systems of the Neutral Type

    On the Controllability to Closed Sets of Nonlinear and Related Linear Systems

    A Discrete-time Nonlinear (m + n(-Person Labor MarketSystem with Uncertainty

    Time Delays in Predator-Prey Systems

    On Selecting a Response Function in Nonlinear Regression

    On the Moments of Exponential Decay

    On the Steady State of an Age Dependent Model for Malaria

    Abstract Volterra Equations with Infinite Delay

    The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations—Analytical Approach

    Sum of Ranges of Operators and Applications

    A Variation of Razumikhin's Method for Retarded Functional Differential Equations

    A Degenerate Problem of Singular Perturbations

    Bôcher-Osgood Type Theorems for Third Order Differential Equations

    On the Characterization of Macromolecular Length Distributions by Analysis of Electrical Birefringence Decay

    Periodic Solutions and Perturbed Semigroups of Linear Operators

    Speculative Demand with Supply Response Lag

    A Geometrical Study of B-Cell Stimulation and Humoral Immune Response

    Generalized Stability of Motion and Vector Lyapunov Functions

    Simple Analogs for Nerve Membrane Equations

    Oscillations Results for a Nonhomogeneous Equation

    The Comparison of a Four-Compartment and a Five-Compartment Model of Rose Bengal Transport through the Hepatic System

    Some Properties of Increasing Densifying Mappings

    Oscillation in a Non-Linear Parabolic Model of Separated, Cooperatively Coupled Enzymes

    Iterative Techniques for Inversion of the Nonlinear Perrin Equations for Diffusion of Spheriods

Product details

  • No. of pages: 716
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: January 28, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9781483272245

About the Editor

V. Lakshmikantham

Affiliations and Expertise

University of Texas at Arlington, USA

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