This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.

V. LAKSHMIKANTHAM is Professor and Chairman in the Department of Mathematics at the University of Texas at Arlington. In addition, he is coeditor of the journal Stochastic Analysis and Applications (Marcel Dekker, Inc.), editor of Nonlinear Analysis, and a member of the editorial boards of six other journals. He is an internationally known mathematician, having published several monographs and over 150 papers in the fields of ordinary and partial differential equations, nonlinear and stochastic analysis, and abstract differential equations.

CONTENTS -- Honoring Professor E. A. Coddington -- Preface -- Contributors -- Unbounded Perturbations and the Existence of Differentiable Solutions of the Cauchy Problem in Banach Space /Nazar Hussein Abdelaziz -- Escape Time by Fixed Point Theorem /A. R. Aftabizadeh -- Asymptotic Behaviour of Solutions of Nth Order Differential Equations with or without Delay /Olusola Akinyele and R. S. Dahiya -- Nonconstant Periodic Solutions of Nonlinear Differential Equations /Shair Ahmad and Francisco Montes de Oca -- Evolution Water Coning Problem /Y. Amirat, A. El Kolli and A. Ziani -- Conditions for Periodic Solutions to Hill?s Equation with an even Periodic Coefficient /Bernard A. Asner, Jr. -- Metrics and Tolerances /Prem N. Bajaj -- Global Existence for Nonlinear Second Order Differential Equations /John V. Baxley -- Asymptotically Nonresonant Nonlinear Equations /Ronald I. Becker -- Boundedness of Oscillatory Solutions of Fourth Order Linear Ordinary Homogeneous Differential Equations /Abdelali Benharbit -- A Neighborhood of the Hopf Singularity /S. R. Bernfeld -- Second Order Differential Systems with Generalized Nonlinear Boundary Conditions /S. R. Bernfeld -- Dynamics and Bifurcation in one Dimension /Louis Block and David Hart -- The Effect of Harvesting on Population Systems /Fred Brauer -- Invariants of Vortex Motions in the Plane /Jacob Burbea -- Instability and Stability in Volterra Equations /T. A. Burton and W. E. Mahfoud -- Alternating Bounds Converging to the Solution of a Semi-linear Euler-Poisson-Darboux Equation /C. Y. Chan -- Comparison Theorems and Stochastic Boundary Value Problems /Jagdish Chandra and G. S. Ladde -- Constrained Global Null Controllability of Nonlinear Delay Systems /Ethelbert N. Chukwu -- Spectral Theory for Symmetric Pairs of Ordinary Differential Operators /Earl A. Coddington -- Almost Periodic Solutions to Some Nonlinear Parabolic Equations /C. Corduneanu -- Conjugate Points and Disconjugacy of Second Order Systems /Fozi M. Dannan -- Some Results on the Existence of Free Boundaries for Parabolic Reaction-Diffusion Systems /Ildefonso Diaz and Jesus Hernandez -- A Neutral System with State-Dependent Delays /R. D. Driver -- Asymptotic Properties of Solutions to a Class of Nonlinear Systems of Differential Equations Arising in Pharmacokinetics and Tracer Kinetics /J. Eisenfeld -- Some Remarks on Semi flows /Saber Elaydi -- A Two Dimensional Model for Turbulence /W. E. Fitzgibbon -- Asymptotic Properties of Inhomogeneous Wave Equations /Jerome A. Goldstein and James T, Sandefur, Jr. -- On a property of Olicz-Sobolev Spaces /J. P. Gossez -- An Optimal L°° Error Estimate for Galerkin Approximations to Solutions of Two-Point Nonlinear Boundary Value Problems /John Gregory and Marvin Zeman -- Quadratic Systems /R. D. S. Grisell -- Continuation Theorems for Nonlinear Equations /Chaitan P. Gupta -- Multiplicative Perturbation of m-Accretive Operators and Evolution Equations in L (ft) /Ki Sik Ha -- Energy Bounds for the Slow Capture by a Center /Richard Haberman -- An Integral Equation for Helminthic Infections: Stability of the Non-Infected Population /K. P. Hadeler -- Asymptotic Analysis of Rudimentary Models of Toxicant-Population Interactions /Thomas G. Hallam -- On the Asymptotic Stability by Lyapunov Function with Semidefinite Derivative /L. Hatvani -- Ergodic Theorems for Nonlinear Volterra Integral Equations /Douglas S. Hulbert and Simeon Reich -- Some Remarks on Continuous and Discrete Flows /S. K. Kaul -- Some Stability Notions /Ronald A. Knight -- Functional Differential Inequalities and Equations with Oscillating Coefficients /G. Ladas, Y. G. Sficas and J. P. Stavroulakis -- The Present State of the Method of Upper and Lower Solutions /V. Lakshmikantham -- On a Conjecture on the Number of Solutions of a Nonlinear Dirichlet Problem with Jumping Nonlinearity /A. C. Lazer and P. J. McKenna -- Operator Parts of Ordinary Differential Subspaces with Application to Nonlinear Problems /Sung J. Lee -- Large-Scale Systems, Cone-Valued Lyapunov Functions and Quasi-Solutions /S. Leela -- A Nonlinear Volterra Integrodifferential Equation Occuring in Heat Flow /S.-0, Londen and J. A. Nohel -- On Exact Controllability in Hilbert Spaces /J.-Cl. Louis and D. Wexler -- Continuous Dependence for Demicompact Maps /Rafiq Makhluf and Zdenek Vorel -- Vector Lyapunov Functions Method in the Analysis of Dynamical Properties of Nonlinear Differential Equations /V. M. Matrosov -- Some Recent Topics on Nonlinear Semi-Groups /Isao Miyadera -- Set Valued Extensions of Integral Inequalities /R. E. Moore -- Equations with Nonlinearities Defined only on Subsets /R. Kent Nagle -- Operator Parts and Generalized Inverses for Linear Manifolds with Applications /Z. Nashed -- Some Global Steepest Descent Results for Nonlinear Systems /John W. Neuberger -- Nonlinear Problems at Resonance via Lyapunov-Like Functions / J. J. Nieto -- Some Problems Concerning Nonlinear Oscillators in Neural Networks /M. Namik Oguztttreli -- An Inclusion Principle for Hereditary Systems /Y. Ohta and D. D. Siljak -- On Critical Case of Liapunov's Stability of One-Degree of Freedom System /Andrzej Olas -- Some Computational Procedures for Nonlinear Problems in /M. C. Pandian -- Monotone Convergence of Time-Dependent Solutions for Coupled Reaction-Diffusion Systems /C. V. Pao -- A Simple Conversion of Two-Point BVP to One Point BVP /Fred R. Payne and Fung-Tai Ko -- Constructive Existence of Solution to a Nonlinear Eigenvalue Problem with Application to Nth Order Reaction Diffusion Problems /W. L. Perry -- A Frequency Domain Approach for Finding the Limit Behavior of Retarded Differential Equations /V. M. Popov -- Labeled Graphs and a Class of Generalized Volterra -- Systems /Ray Redheffer -- The Method of Quasi Upper and Lower Solutions for Extremal Solutions of Volterra Integral Equations in Abstract Cones /G. R. Shendge -- Perturbed Bifurcation Theory for a Class of Autonomous Ordinary Differential Equations /Ratnasingham Shivaji -- Bifurcation of Subharmonic Solutions for a Periodic Epidemic Model /Hal L. Smith -- Some Comparison and Convergence Theorems in X(n,k)-Parameter Families /S. Umamaheswaram -- Obstructions to the Existence of Transverse Volume Elements of Foliations /J. Vaisman -- The Monotone Method for a Second-Order Differential Equation /C. Vargas -- Existence of Coupled Minimal and Maximal Periodic Quasisolutions for Systems of First Order PBVP via Quasisolutions /A. S. Vatsala -- Differential Equations with Piecewise Constant Delays /Joseph Wiener -- Asymptotic Behavior of Solutions in Nonautonomous Systems /Taro Yoshizawa.