Trends in Theory and Practice of Nonlinear Differential Equations  book cover
1st Edition

Trends in Theory and Practice of Nonlinear Differential Equations

ISBN 9780824771300
Published January 3, 1984 by CRC Press
592 Pages

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Book Description

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.

Table of Contents

1. Unbounded Perturbations and the Existence of Differentiable Solutions of the Cauchy Problem in Banach Space 2. Escape Time by Fixed Point Theorem 3. Asymptotic Behaviour of Solutions of Nth Order Differential Equations with or without Delay 4. Nonconstant Periodic Solutions of Nonlinear Differential Equations 5. Evolution Water Coming Problem 6. Conditions for Periodic Solutions to Hill’s Equation with an even Periodic Coefficient 7. Metrics and Tolerances 8. Global Existence for Nonlinear Second Order Differential Equations 9. Asymptotically Nonresonant Nonlinear Equations 10. Boundedness of Oscillatory Solutions of Fourth Order Linear Ordinary Homogeneous Differential Equations Abdelali Benharbit 11. A Neighborhood of the Hopf Singularity 12. Second Order Differential Systems with Generalized Nonlinear Boundary Conditions 13. Dynamics and Bifurcation in one Dimension 14. The Effect of Harvesting on Population Systems 15. Invariants of Vortex Motions in the Plane 16. Instability and Stability in Volterra Equations 17. Alternating Bounds Converging to the Solution of a Semilinear Euler—Poisson—Darboux Equation 18. Comparison Theorems and Stochastic Boundary Value Problems 19. Constrained Global Null Controllability of Nonlinear Delay Systems 20. Spectral Theory for Symmetric Pairs of Ordinary Differential Operators 21. Almost Periodic Solutions to Some Nonlinear Parabolic Equations 22. Conjugate Points and Disconjugacy of Second Order Systems 23. Some Results on the Existence of Free Boundaries for Parabolic Reaction—Diffusion Systems 24. A Neutral System with State—Dependent Delays 25. Asymptotic Properties of Solutions to a Class of Nonlinear Systems of Differential Equations Arising in Pharmacokinetics and Tracer Kinetics 26. Some Remarks on Semi flows 27. A Two Dimensional Model for Turbulence 28. Asymptotic Properties of Inhomogeneous Wave Equations 29. On a property of Olicz—Sobolev Spaces 30. An Optimal L∞ Error Estimate for Galerkin Approximations to Solutions of Two—Point Nonlinear Boundary Value Problems 31. Quadracic Systems 32. Continuation Theorems for Nonlinear Equations 33. Multiplicative Perturbatin of m—Accretive Operators and Evolution Equations in L∞ (Ω) 34. Energy Bounds for the Slow Capture by a Center 35. An Integral Equation for Helminthic Infections: Stability of the Non—Infected Population 36. Asymptotic Analysis of Rudimentary Models of Toxicant—Population Interactions 37. On the Asymptotic Stability by Lyapunov Function with Semidefinite Derivative 38. Ergodic Theorems for Nonlinear Volterra Integral Equations 39. Some Remarks on Continuous and Discrete Flows 40. Some Stability Notions 41. Functional Differential Inequalities and Equations with Oscillating Coefficients 42. The Present State of the Method of Upper and Lower Solutions 43. On a Conjecture on the Number of Solutions of a Nonlinear Dirichlet Problem with Jumping Nonlinearity 44. Operator Parts of Ordinary Differential Subspaces with Application to Nonlinear Problems 45. Large—Scale Systems, Cone—Valued Lyapunov Functions and Quasi—Solutions 46. A Nonlinear Volterra Integrodifferential Equation Occuring in Heat Flow 47. On Exact Controllability in Hilbert Spaces 48. Continuous Dependence for Demicompact Maps 49. Vector Lyapunov Functions Method in the Analysis of Dynamical Properties of Nonlinear Differential Equations 50. Some Recent Topics on Nonlinear Semi—Groups 51. Set Valued Extensions of Integral Inequalities 52. Equations with Nonlinearities Defined only on Subsets 53. Operator Parts and Generalized Inverses for Linear Manifolds with Applications 54. Some Global Steepest Descent Results for Nonlinear Systems 55. Nonlinear Problems at Resonance via Lyapunov—Like Functions 56. Some Problems Concerning Nonlinear Oscillators in Neural Networks 57. An Inclusion Principle for Hereditary Systems 58. On Critical Case of Liapunov’s Stability of One—Degree of Freedom System 59. Some Computational Procedures for Nonlinear Problems in Rn 60. Monotone Convergence of Time—Dependent Solutions for Coupled Reaction—Diffusion Systems 61. A Simple Conversion of Two—Point BVP to One Point BVP 62. Constructive Existence of Solution to a Nonlinear Eigen—value Problem with Application to Nth Order Reaction Diffusion Problems 63. A Frequency Domain Approach for Finding the Limit Behavior of Retarded Differential Equations 64. Labeled Graphs and a Class of Generalized Volterra Systems 65. The Method of Quasi Upper and Lower Solutions for Extremal Solutions of Volterra Integral Equations in Abstract Cones 66. Perturbed Bifurcation Theory for a Class of Autonomous Ordinary Differential Equations 67. Bifurcation of Subharmonic Solutions for a Periodic Epidemic Model 68. Some Comparison and Convergence Theorems in λ(n,k)—Parameter Families 69. Obstructions to the Existence of Transverse Volume Elements of Foliations 70. The Monotone Method for a Second—Order Differential Equation 71. Existence of Coupled Minimal and Maximal Periodic Quasi— solutions for Systems of First Order PBVP via Quasisolutions 72. Differential Equations with Piecewise Constant Delays 73. Asymptotic Behavior of Solutions in Nonautonomous Systems

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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.