Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences.
In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques.
This book will be helpful to students, practitioners, and researchers in the field of mathematics.

ContributorsPrefaceHonoring Professor Lamberto CesariInvited Addresses and Research Reports Group Properties of un = [f(u)ux]x Perturbation and Bifurcation in a Discontinuous Nonlinear Eigenvalue Problem A Singular Fourier Problem with Nonlinear Boundary Condition Diversity and Spatial Effects on Competitive Systems A Bang-Bang Type Theorem for Measures Some Optimal Control Problems for the Helmholtz Equation Stability of a Large Flexible Beam in Space Some Constructions in Semi-Dynamical Systems Identification of Nonlinear Delay Systems Using Spline Methods Parameter Estimation Techniques for Nonlinear Distributed Parameter Systems Projection Techniques for Nonlinear Elliptic PDE An Operational Equation Arising in Synthesis of Optimal Control The Problem of Graffi-Cesari A Variational Approach to Solving Semilinear Equations at Resonance Exchange of Stability and Hopf Bifurcation Monotone Method for Nonlinear Boundary Value Problems by Linearization Techniques Existence and Uniqueness of Solutions to Nonlinear-Operator-Differential Equations Generalizing Dynamical Systems of Automatic Spaceship Navigation A Numerical Method for a Free Surface Density-Driven Flow Vortex Motions and Their Stability The Hamilton-Jacobi Equation with an Unbounded Inhomogeneity Finite Difference Methods for Identification of Hereditary Control Systems Models of Vertically Transmitted Diseases with Sequential-Continuous Dynamics Vertically Transmitted Diseases A Stochastic Compartimentai Model of Preinfarction Angina A Nonlinear Diffusion System Modelling the Spread of Oro-Faecal Diseases Existence of Solutions of Hyperbolic Problems Applications of Differential Inequalities to Gas Lubrication Theory Comparison Principle and Theory of Nonlinear Boundary Value Problems Differential Equations with Discontinuous Nonlinearities An Estimate for the Solution of a Certain Functional Differential Equation of Neutral Type A Semidiscretization Procedure for Fitzhugh-Nagumo Equations Bifurcation of Periodic Solutions of Nonlinear Equations in Age-Structured Population Dynamics Conservation Laws with Dissipation On Fixed Points of Multivalued Maps Bifurcation of Stable Periodic Solutions for Periodic Quasilinear Parabolic Equations Continuity of Weak Solutions to Certain Singular Parabolic Equations A Problem Arising in the Mathematical Theory of Epidemics A Collinear A7-Body Problem of Classical Electrodynamics On Qualitative Properties of Nonlinear Compartmental Systems The Asymptotic Form of Nonoscillatory Solutions to Fourth-Order Equations Identification of Nonlinear Compartmental Systems with an Application to the Modelling of the Enzyme Cytochrome P-450 Some Applications of Hadamard's Inverse Function Theorem Comparison Theorems for Riccati Differential Equations in a B*-Algebra Oscillations Périodiques des Systèmes Mécaniques Non Lineaires Excitées par des Distributions d (Percussions) ou d' Representation and Asymptotic Behavior of Strongly DampedEvolution Equations Degree Theoretic Methods in Optimal Control A Galerkin Numerical Method for a Class of Nonlinear Reaction-Diffusion Systems On a Semi-Coercive Quasi-Variational Inequality A Threshold Model of Antigen Antibody Dynamics with Fading Memory One Phenomenon in Nonlinear Oscillations Two Fixed Point Principles Cheap Shooting Methods for Self-Adjoint Problems Using Initial Value Methods On Entire Solutions in Some Nonlinear Fourth-Order Elliptic Equations On the Existence of Large Amplitude Plane-Polarized Alfven Waves Direct Computer Simulation of Nonlinear Waves in Solids, Liquids, and Gases Functional Equations of Fredholm-Type and Nonlinear Boundary Value Problems On Structural Identification Recent Results for Wave Equations of Rayleigh and Van der Pol Type