This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.

V. Lakshmikantham is Professor, and was Chairman of the Department of Mathematics (1973-1986), at The University of Texas at Arlington. He is founder and editor of the journal Nonlinear Analysis: Theory, Methods, and Applications, as well as coeditor (with G.S. Ladde) of the journal Stochastic Analysis and Applications (Marcel Dekker, Inc.). Dr. Lakshmikantham is also editor of Trends in Theory and Practice of Nonlinear Differential Equations, and coauthor (with G.S. Ladde andB.G. Zhang) of Oscillation Theory of Differential Equations with Deviating Arguments (both books, Marcel Dekker, Inc.). He is the author of several other books and associate editor of six journals. He has written over 200 research papers. He received the M.A. (1955) and Ph.D. (1957) degrees from Osmania University, Hyderabad, India.

Honoring Professor V. Lakshmikantham -- Preface -- Contributors -- New Results on Local Existence for Quasilinear Parabolic Systems -- Paolo Acquistapace -- A New Analysis for Nonlinear Systems /G. Adomian -- Oscillatory and Periodic Solutions of Advanced Differential Equations with Piecewise Constant Argument /A.R. Aftabizadeh and Joseph Wiener -- Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Space /N.U. Ahmed -- Time-Dependent Volterra Equations in Hilbert Space /Sergiu Aizicovici -- The Superposition Operator in Spaces of Measurable and Continuous Functions /Jurgen Appell -- Generalized Singular Points in Products of Semi-dynamical Systems /Prem N. Bajaj -- Hopf Bifurcation for Two Dimensional Periodic Differential Systems /S.R. Bernf'eld -- Change of Sign of the Solutions to Some Parabolic Problems /F. Bernis -- Existence of a Solution to a Nonlinear Elliptic Problem in Non Variational Form /Marco Biroli -- On Integral Transforms Appearing in the Derivation of the Equations of an Aeroelastic System /John A, Bums, Eugene M. Cliff, Terry L. Herdman and Janos Turi -- Krasovskii's Stability Theory /To A. Burton, A. Casal and A. Somolinos -- Consequences of the Duality Map Taking Planes to Planes /Bruce D. Calvert and Simon Fitzpatrick -- A Nonlinear Singular Parabolic Initial Boundary Value Problem /C.Y. Chan and C.S. Chen -- On the Monotone Iterative Technique for Nonlinear Volterra Type Integro-Differential Equation in Banach Space /Yubo Chen -- The Time Optimal Control Theory of Nonlinear Systems of Neutral Type /E.N. Chukwu -- A Singular Perturbation Approach to Abstract Volterra Equations /Constantin Corduneanu -- Efficient Numerical Methods for Optimal Control Problems Via the Calculus of Variations /Bohan Dalpatadu and John Gregory -- Limiting Temperature Jumps in Surface Controlled Exothermic Reactions /Paul Davis and Jagdish Chandra -- Some Open Problems in Ordinary Differential Equations and Fixed Points of (Weakly Inward) Maps in Banach Spaces /Klaus Deimling -- Stability Analysis of Continuous Dynamical Systems with Discrete Controllers /W. Desch, A.N, Michel, B.K. Miller and M. Mousa -- Semilinear Elliptic Equations in Rn /Allan L. Edelson -- Some Remarks on Nonlinear Dichotomy and Trichotomy /S. Elaydi and 0. HcCjek -- Boundary Value Problems for Second Order Differential Equations /L. Erbe and K. Schmitt -- A System of Functional Differential Equations Modeling Threshold Phenomena /J.A. Gatica and P. Waltman -- Degenerate Nonlinear Parabolic Boundary Problems /Jerome A, Goldstein and Chin-Yuan Lin -- Coupling Induced Instability of Synchronous Oscillations /K. Gopalsamy -- Particle Modeling by Systems of Nonlinear Ordinary Differential Equationss /Donald Greenspan -- Some Fixed Point Theorems of Expansion and Compression Type with Applications /Dajun Guo -- Boundary Value Problems Involving Reflection of the Argument /Chaitan P. Gupta -- On a Theorem of Elias for Difference Equations /Darrel Hankerson and Allan Peterson -- Local Controllability of a Single Input, Affine System /H. Hermes and Matthias Kawski -- A Bifurcation Theorem for Nonlinear Equations /Huang Wenzao -- Nonlinear Input-Output Systems /L.R. Hunt, Mladen Luksio and Reno eng Su -- Least-Squares Finite Element Approximation of Nonlinear Problems /B.N. Jiang and G.F. Carey -- The Method of Mixed Monotony and Second Order Boundary Value Problems /Mohammad Khavanin and V. Lakshmikantham -- Numerical Solutions to Stochastic Difference Equations /G.S. Ladde and M. Sambandham -- On Near-Optimum Regulators for Large Scale Systems /G.S. Ladde and 0. Sirisaengtaksin -- On the Existence of a Solution to an It6-Volterra Equation /Marica Lewin -- Positive Solutions of Steady States of Predator-Prey Systems /Lige Li -- The Differentiability of Semigroups Generated by w-Accretive Operators /Guizhong Liu -- On the Local Dynamical System Associated to a Fully Nonlinear Abstract Parabolic Equation /Alessandra Lunardi -- A Fully Nonlinear Boundary Value Problem for the LaPlace Equation /Rolando Magnanini -- Converting a Min-Max Problem into a State Constrained Problem /Negash G. Medhin -- Singular Nonlinear Oscillator Equations /Ronald E. Mickens -- Variational Approach to Differential Equations and Representation of Lagrangians in Certain Biological Models /K.N. Murty -- On Nonlinear Ill-Posed Problems I: Classes of Operator Equations and Minimization of Functionals /M. Z. Nashed -- A Maximum Principle in Nonlinear Fourth Order Elliptic Equations /Edward C. Nichols and Philip W. Schaefer -- Hukahara-Kneser Property for Nonlinear Boundary Value Problems /Juan J. Nieto -- A Qualitative Analysis of a Class of Gas-Solid Reactions /N. Namik Oguztoreli and Baki 'Ozum -- Fixed Points of Multi-Mappings Related to Minimization Problems /D.V. Pai and S.A Naimpally -- Periodic Kolmogorov Biological Systems /Houyao Pan and Zhiming Zhou -- Monotone Methods for Numerical Solution of Reaction-Diffusion Equations /C.V. Pao -- An Optimal (?) Elliptic Solver /Fred R. Payne and. Moshen Mahmoudi -- Some Qualitative Problems in the Theory of Partial Differential Equations /Andrzej Pelczar -- About Linearization, Conization, Calmness, Openness and Regularity /Jean-Paul Penot -- A New and Unified Theorem for the Solvability of xGT(x) in Cones with T k-Set-Contractive /W. V. Petryshyn -- Quasilinear Systems, Semigroups and Nonlinear Coupling /George H. Pimbley -- Bounded Solutions of Nonlinear Hyperbolic Equations with Delay /H. Poorkarimi and J. Wiener -- Left Subinverses and Monotone Iterations for Nonlinear Operator Equations /Florian A. Potra -- A Positivity Method for Linear Volterra Equations /Jan Pruss -- Equations for the Dynamics of a Josephson Junction and a Phase-Locked Loop /Qian Min and Zhang Jinyan -- Stochastic Systems Under Quadratic Payoff /A.N.V. Rao and Chris P. Tsokos -- M -Stability for Integro-Differential Equations /M. Rama Mohana Rao -- Integral Equations, Hyperconvex Spaces and the Hilbert Ball /Simeon Reich -- Free Boundary Stability in the One Phase Stefan Problem /Jose* Francisco Rodrigues -- Reachable Sets, Limit Sets and Holding Sets in Control Systems /Emilio 0. Roxin -- Invariant Spectral Manifolds and Normal Form for the Navier-Stokes Equations with Potential Forces /Jean-Claude Saut -- Oscillation of Solutions of a Population Equation with Delay /George Seifert -- Existence of Solutions to Volterra Functional Integral Equations with Infinite Delay /Seppo Seikkala -- A Remark on the Existence of Three Solutions via Sub-Super Solutions /Ratnasingham Shivaji -- The Method of Upper and Lower Solutions and the Interval Method for Second Order Differential Equations /S. Sivasundaram -- A Note on the Hartman-Stampacchia Theorem /Michel Thera -- Monotone Iterative Technique for Singular Systems of Differential Equations /A. S. Vatsala -- Multidimensional Solitary Waves: Explicit Examples and Scattering Theory /Henry A. Warohall -- The Regularity of Minimizers /S.Walter Wei -- Control of Beams and Plates: Location of Actuators /L.W. White -- Some Results on Equations with Unbounded Delay /Taro Yoshizawa -- 3-Dimensional Gradient Conjugate Systems and its Applications /Zhang Jinyan -- What Inflences on the Number of Limit Cycles of Li£nard Equation /Zhang Zhifen -- Some Fundamental Properties of Solutions for Initial Value Problem of Nonlinear Volterra Type Integro-Differential Equation in Abstract Spaces /Wan Zhuang -- Nonatomic Neutral Functional Differential Equations /John A. Burns> Terry L. Herdman and Janos Turi -- Index.