nonlinear analysis and applications

V. Lakshmikantham, Lakshmikantham

• Publisher: CRC Press
• Year: 2020
• Print ISBN:
  9780824778101
• eBook ISBN:
  9781000147032
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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.

Contents

1. Honoring Professor V. Lakshmikantham
2. Preface
3. Contributors
4. New Results on Local Existence for Quasilinear Parabolic Systems
   Paolo Acquistapace
5. A New Analysis for Nonlinear Systems
   G. Adomian
6. Oscillatory and Periodic Solutions of Advanced Differential Equations with Piecewise Constant Argument
   A.R. Aftabizadeh and Joseph Wiener
7. Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Space
   N.U. Ahmed
8. Time-Dependent Volterra Equations in Hilbert Space
   Sergiu Aizicovici
9. The Superposition Operator in Spaces of Measurable and Continuous Functions
   Jürgen Appell
10. Generalized Singular Points in Products of Semi-dynamical Systems
    Prem N. Bajaj
11. Hopf Bifurcation for Two Dimensional Periodic Differential Systems
    S.R. Bernfeld
12. Change of Sign of the Solutions to Some Parabolic Problems
    F. Bernis
13. Existence of a Solution to a Nonlinear Elliptic Problem in Non Variational Form
    Marco Biroli
14. On Integral Transforms Appearing in the Derivation of the Equations of an Aeroelastic System
    John A. Burns, Eugene M. Cliff, Terry L. Herdman and Janos Turi
15. Krasovskii's Stability Theory
    T.A. Burton, A. Casal and A. Somolinos
16. Consequences of the Duality Map Taking Planes to Planes
    Bruce D. Calvert and Simon Fitzpatrick
17. A Nonlinear Singular Parabolic Initial Boundary Value Problem
    C.Y. Chan and C.S. Chen
18. On the Monotone Iterative Technique for Nonlinear Volterra Type Integro-Differential Equation in Banach Space
    Yubo Chen
19. The Time Optimal Control Theory of Nonlinear Systems of Neutral Type
    E.N. Chukwu
20. A Singular Perturbation Approach to Abstract Volterra Equations
    Constantin Corduneanu
21. Efficient Numerical Methods for Optimal Control Problems Via the Calculus of Variations
    Rohan Dalpatadu and John Gregory
22. Limiting Temperature Jumps in Surface Controlled Exothermic Reactions
    Paul Davis and Jagdish Chandra
23. Some Open Problems in Ordinary Differential Equations and Fixed Points of (Weakly Inward) Maps in Banach Spaces
    Klaus Deimling
24. Stability Analysis of Continuous Dynamical Systems with Discrete Controllers
    W. Desch, A.N. Michel, R.K. Miller and M. Mousa
25. Semilinear Elliptic Equations in Rⁿ
    Allan L. Edelson
26. Some Remarks on Nonlinear Dichotomy and Trichotomy
    S. Elaydi and O. Hájek
27. Boundary Value Problems for Second Order Differential Equations
    L. Erbe and K. Schmitt
28. A System of Functional Differential Equations Modeling Threshold Phenomena
    J.A. Gatica and P. Waltman
29. Degenerate Nonlinear Parabolic Boundary Problems
    Jerome A. Goldstein and Chin-Yuan Lin
30. Coupling Induced Instability of Synchronous Oscillations
    K. Gopalsamy
31. Particle Modeling by Systems of Nonlinear Ordinary Differential Equations
    Donald Greenspan
32. Some Fixed Point Theorems of Expansion and Compression Type with Applications
    Dajun Guo
33. Boundary Value Problems Involving Reflection of the Argument
    Chaitan P. Gupta
34. On a Theorem of Elias for Difference Equations
    Darrel Hankerson and Allan Peterson
35. Local Controllability of a Single Input, Affine System
    H. Hermes and Matthias Kawski
36. A Bifurcation Theorem for Nonlinear Equations
    Huang Wenzao
37. Nonlinear Input-Output Systems
    L.R. Hunt, Mladen Luksic and Renjeng Su
38. Least-Squares Finite Element Approximation of Nonlinear Problems
    B.N. Jiang and G.F. Carey
39. The Method of Mixed Monotony and Second Order Boundary Value Problems
    Mohammad Khavanin and V. Lakshmikantham
40. Numerical Solutions to Stochastic Difference Equations
    G.S. Ladde and M. Sambandham
41. On Near-Optimum Regulators for Large Scale Systems
    G.S. Ladde and O. Sirisaengtaksin
42. On the Existence of a Solution to an Itô-Volterra Equation
    Marica Lewin
43. Positive Solutions of Steady States of Predator-Prey Systems
    Lige Li
44. The Differentiability of Semigroups Generated by ω-Accretive Operators
    Guizhong Liu
45. On the Local Dynamical System Associated to a Fully Nonlinear Abstract Parabolic Equation
    Alessandra Lunardi
46. A Fully Nonlinear Boundary Value Problem for the LaPlace Equation
    Rolando Magnanini
47. Converting a Min-Max Problem into a State Constrained Problem
    Negash G. Medhin
48. Singular Nonlinear Oscillator Equations
    Ronald E. Mickens
49. Variational Approach to Differential Equations and Representation of Lagrangians in Certain Biological Models
    K.N. Murty
50. On Nonlinear Ill-Posed Problems I: Classes of Operator Equations and Minimization of Functionals
    M.Z. Nashed
51. A Maximum Principle in Nonlinear Fourth Order Elliptic Equations
    Edward C. Nichols and Philip W. Schaefer
52. Hukahara-Kneser Property for Nonlinear Boundary Value Problems
    Juan J. Nieto
53. A Qualitative Analysis of a Class of Gas-Solid Reactions
    N. Namik Oǧuztӧreli and Baki Ӧzüm
54. Fixed Points of Multi-Mappings Related to Minimization Problems
    D.V. Pai and S.A Naimpally
55. Periodic Kolmogorov Biological Systems
    Houyao Pan and Zhiming Zhou
56. Monotone Methods for Numerical Solution of Reaction-Diffusion Equations
    C.V. Pao
57. An Optimal (?) Elliptic Solver
    Fred R. Payne and Moshen Mahmoudi
58. Some Qualitative Problems in the Theory of Partial Differential Equations
    Andrzej Pelczar
59. About Linearization, Conization, Calmness, Openness and Regularity
    Jean-Paul Penot
60. A New and Unified Theorem for the Solvability of x ϵ T(x) in Cones with T k-Set-Contractive
    W.V. Petryshyn
61. Quasilinear Systems, Semigroups and Nonlinear Coupling
    George H. Pimbley
62. Bounded Solutions of Nonlinear Hyperbolic Equations with Delay
    H. Poorkarimi and J. Wiener
63. Left Subinverses and Monotone Iterations for Nonlinear Operator Equations
    Flo...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Honoring Professor V. Lakshmikantham
• Preface
• Contents
• Contributors
• New Results on Local Existence for Quasilinear Parabolic Systems
• A New Analysis for Nonlinear Systems
• Oscillatory and Periodic Solutions of Advanced Differential Equations with Piecewise Constant Argument
• Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Space
• Time-Dependent Volterra Equations in Hilbert Space
• The Superposition Operator in Spaces of Measurable and Continuous Functions
• Generalized Singular Points in Products of Semi-dynamical Systems
• Hopf Bifurcation for Two Dimensional Periodic Differential Systems
• Change of Sign of the Solutions to Some Parabolic Problems
• Existence of a Solution to a Nonlinear Elliptic Problem in Non Variational Form
• On Integral Transforms Appearing in the Derivation of the Equations of an Aeroelastic System
• Krasovskii's Stability Theory
• Consequences of the Duality Map Taking Planes to Planes
• A Nonlinear Singular Parabolic Initial Boundary Value Problem
• On the Monotone Iterative Technique for Nonlinear Volterra Type Integro-Differential Equation in Banach Space
• The Time Optimal Control Theory of Nonlinear Systems of Neutral Type
• A Singular Perturbation Approach to Abstract Volterra Equations
• Efficient Numerical Methods for Optimal Control Problems Via the Calculus of Variations
• Limiting Temperature Jumps in Surface Controlled Exothermic Reactions
• Some Open Problems in Ordinary Differential Equations and Fixed Points of (Weakly Inward) Maps in Banach Spaces
• Stability Analysis of Continuous Dynamical Systems with Discrete Controllers
• Semilinear Elliptic Equations in Rn
• Some Remarks on Nonlinear Dichotomy and Trichotomy
• Boundary Value Problems for Second Order Differential Equations
• A System of Functional Differential Equations Modeling Threshold Phenomena
• Degenerate Nonlinear Parabolic Boundary Problems
• Coupling Induced Instability of Synchronous Oscillations
• Particle Modeling by Systems of Nonlinear Ordinary Differential Equations
• Some Fixed Point Theorems of Expansion and Compression Type with Applications
• Boundary Value Problems Involving Reflection of the Argument
• On a Theorem of Elias for Difference Equations
• Local Controllability of a Single Input, Affine System
• A Bifurcation Theorem for Nonlinear Equations
• Nonlinear Input-Output Systems
• Least-Squares Finite Element Approximation of Nonlinear Problems
• The Method of Mixed Monotony and Second Order Boundary Value Problems
• Numerical Solutions to Stochastic Difference Equations
• On Near-Optimum Regulators for Large Scale Systems
• On the Existence of a Solution to an Itô-Volterra Equation
• Positive Solutions of Steady States of Predator-Prey Systems
• The Differentiability of Semigroups Generated by ω-Accretive Operators
• On the Local Dynamical System Associated to a Fully Nonlinear Abstract Parabolic Equation
• A Fully Nonlinear Boundary Value Problem for the LaPlace Equation
• Converting a Min-Max Problem into a State Constrained Problem
• Singular Nonlinear Oscillator Equations
• Variational Approach to Differential Equations and Representation of Lagrangians in Certain Biological Models
• On Nonlinear Ill-Posed Problems I: Classes of Operator Equations and Minimization of Functionals
• A Maximum Principle in Nonlinear Fourth Order Elliptic Equations
• Hukahara-Kneser Property for Nonlinear Boundary Value Problems
• A Qualitative Analysis of a Class of Gas-Solid Reactions
• Fixed Points of Multi-Mappings Related to Minimization Problems
• Periodic Kolmogorov Biological Systems
• Monotone Methods for Numerical Solution of Reaction-Diffusion Equations
• An Optimal (?) Elliptic Solver
• Some Qualitative Problems in the Theory of Partial Differential Equations
• About Linearization, Conization, Calmness, Openness and Regularity
• A New and Unified Theorem for the Solvability of x ϵ T(x) in Cones with T k-Set-Contractive
• Quasilinear Systems, Semigroups and Nonlinear Coupling
• Bounded Solutions of Nonlinear Hyperbolic Equations with Delay
• Left Subinverses and Monotone Iterations for Nonlinear Operator Equations
• A Positivity Method for Linear Volterra Equations
• Equations for the Dynamics of a Josephson Junction and a Phase-Locked Loop
• Stochastic Systems Under Quadratic Payoff
• M0-Stability for Integro-Differential Equations
• Integral Equations, Hyperconvex Spaces and the Hilbert Ball
• Free Boundary Stability in the One Phase Stefan Problem
• Reachable Sets, Limit Sets and Holding Sets in Control Systems
• Invariant Spectral Manifolds and Normal Form for the Navier-Stokes Equations with Potential Forces
• Oscillation of Solutions of a Population Equation with Delay
• Existence of Solutions to Volterra Functional Integral Equations with Infinite Delay
• A Remark on the Existence of Three Solutions via Sub-Super Solutions
• The Method of Upper and Lower Solutions and the Interval Method for Second Order Differential Equations
• A Note on the Hartman-Stampacchia Theorem
• Monotone Iterative Technique for Singular Systems of Differential Equations
• Multidimensional Solitary Waves: Explicit Examples and Scattering Theory
• The Regularity of Minimizers
• Control of Beams and Plates: Location of Actuators
• Some Results on Equations with Unbounded Delay
• 3-Dimensional Gradient Conjugate Systems and its Applications
• What Inflences on the Number of Limit Cycles of Liénard Equation
• Some Fundamental Properties of Solutions for Initial Value Problem of Nonlinear Volterra Type Integro-Differential Equation in Abstract Spaces
• Nonatomic Neutral Functional Differential Equations
• Index