# nonlinear analysis and applications

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## Book Description

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.

## Table of Contents

1. New Results on Local Existence for Quasilinear Parabolic Systems 2. A New Analysis for Nonlinear Systems 3. Oscillatory and Periodic Solutions of Advanced Differential Equations with Piecewise Constant Argument 4. Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Space 5. Time-Dependent Volterra Equations in Hilbert Space 6. The Superposition Operator in Spaces of Measurable and Continuous Functions 7. Generalized Singular Points in Products of Semi-dynamical Systems 8. Hopf Bifurcation for Two Dimensional Periodic Differential Systems 9. Change of Sign of the Solutions to Some Parabolic Problems 10. Existence of a Solution to a Nonlinear Elliptic Problem in Non Variational Form 11. On Integral Transforms Appearing in the Derivation of the Equations of an Aeroelastic System 12. Krasovskii's Stability Theory 13. Consequences of the Duality Map Taking Planes to Planes 14. A Nonlinear Singular Parabolic Initial Boundary Value Problem 15. On the Monotone Iterative Technique for Nonlinear Volterra Type Integro-Differential Equation in Banach Space 16. The Time Optimal Control Theory of Nonlinear Systems of Neutral Type 17. A Singular Perturbation Approach to Abstract Volterra Equations 18. Efficient Numerical Methods for Optimal Control Problems via the Calculus of Variations 19. Limiting Temperature Jumps in Surface Controlled Exothermic Reactions 20. Some Open Problems in Ordinary Differential Equations and Fixed Points of (Weakly Inward) Maps in Banach Spaces 21. Stability Analysis of Continuous Dynamical Systems with Discrete Controllers 22. Semilinear Elliptic Equations in Rn 23. Some Remarks on Nonlinear Dichotomy and Trichotomy 24. Boundary Value Problems for Second Order Differential Equations 25. A System of Functional Differential Equations Modeling Threshold Phenomena 26. Degenerate Nonlinear Parabolic Boundary Problems 27. Coupling Induced Instability of Synchronous Oscillations 28. Particle Modeling by Systems of Nonlinear Ordinary Differential Equations 29. Some Fixed Point Theorems of Expansion and Compression Type with Applications 30. Boundary Value Problems Involving Reflection of the Argument 31. On a Theorem of Elias for Difference Equations 32. Local Controllability of a Single Input, Affine System 33. A Bifurcation Theorem for Nonlinear Equations 34. Nonlinear Input-Output Systems 35. Least-Squares Finite Element Approximation of Nonlinear Problems 36. The Method of Mixed Monotony and Second Order Boundary Value Problems 37. Numerical Solutions to Stochastic Difference Equations 38. On Near-Optimum Regulators for Large Scale Systems 39. On the Existence of a Solution to an Itδ-Volterra Equation 40. Positive Solutions of Steady States of Predator-Prey Systems 41. The Differentiability of Semigroups Generated by ω-Accretive Operators 42. On the Local Dynamical System Associated to a Fully Nonlinear Abstract Parabolic Equation 43. A Fully Nonlinear Boundary Value Problem for the Laplace Equation 44. Converting a Min-Max Problem into a State Constrained Problem 45. Singular Nonlinear Oscillator Equations 46. Variational Approach to Differential Equations and Representation of Lagrangians in Certain Biological Models 47. On Nonlinear Ill-Posed Problems I: Classes of Operator Equations and Minimization of Functionals 48. A Maximum Principle in Nonlinear Fourth Order Elliptic Equations 49. Hukahara-Kneser Property for Nonlinear Boundary Value Problems 50. A Qualitative Analysis of a Class of Gas-Solid Reactions 51. Fixed Points of Multi-Mappings Related to Minimization Problems 52. Periodic Kolmogorov Biological Systems 53. Monotone Methods for Numerical Solution of Reaction-Diffusion Equations 54. An Optimal (?) Elliptic Solver 55. Some Qualitative Problems in the Theory of Partial Differential Equations 56. About Linearization, Conization, Calmness, Openness and Regularity 57. New and Unified Theorem for the Solvability of xϵT(x) in Cones with T k-Set-Contractive 58. Quasilinear Systems, Semigroups and Nonlinear Coupling 59. Bounded Solutions of Nonlinear Hyperbolic Equations with Delay 60. Left Subinverses and Monotone Iterations for Nonlinear Operator Equations 61. A Positivity Method for Linear Volterra Equations 62. Equations for the Dynamics of a Josephson Junction and a Phase-Locked Loop 63. Stochastic Systems Under Quadratic Payoff 64. M -Stability for Integro-Differential Equations Mo 65. Integral Equations, Hyperconvex Spaces and the Hilbert Ball 66. Free Boundary Stability in the One Phase Stefan Problem 67. Reachable Sets, Limit Sets and Holding Sets in Control Systems 68. Invariant Spectral Manifolds and Normal Form for the Navier-Stokes Equations with Potential Forces 69. Oscillation of Solutions of a Population Equation with Delay 70. Existence of Solutions to Volterra Functional Integral Equations with Infinite Delay 71. A Remark on the Existence of Three Solutions via Sub-Super Solutions 72. The Method of Upper and Lower Solutions and the Interval Method for Second Order Differential Equations 73. A Note on the Hartman-Stampacchia Theorem 74. Monotone Iterative Technique for Singular Systems of Differential Equations 75. Multidimensional Solitary Waves: Explicit Examples and Scattering Theory 76. The Regularity of Minimizers 77. Control of Beams and Plates: Location of Actuators 78. Some Results on Equations with Unbounded Delay 79. 3-Dimensional Gradient Conjugate Systems and its Applications 80. What Inflences on the Number of Limit Cycles of Lienhard Equation 81. Some Fundamental Properties of Solutions for Initial Value Problem of Nonlinear Volterra Type Integro-Differential Equation in Abstract Spaces 82. Nonatomic Neutral Functional Differential Equations

## Author(s)

### Biography

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.