Produktbild: Generalized Ordinary Differential Equations in Abstract Spaces and Applications

Generalized Ordinary Differential Equations in Abstract Spaces and Applications Application

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

26.08.2021

Herausgeber

Everaldo M. Bonotto + weitere

Verlag

John Wiley & Sons Inc

Seitenzahl

512

Maße (L/B/H)

23.5/15.7/3.2 cm

Gewicht

887 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-65493-3

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

26.08.2021

Herausgeber

Verlag

John Wiley & Sons Inc

Seitenzahl

512

Maße (L/B/H)

23.5/15.7/3.2 cm

Gewicht

887 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-65493-3

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Generalized Ordinary Differential Equations in Abstract Spaces and Applications
  • List of Contributors xi

    Foreword xiii

    Preface xvii

    1 Preliminaries 1
    Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, Jaqueline G. Mesquita, and Eduard Toon

    1.1 Regulated Functions 2

    1.1.1 Basic Properties 2

    1.1.2 Equiregulated Sets 7

    1.1.3 Uniform Convergence 9

    1.1.4 Relatively Compact Sets 11

    1.2 Functions of Bounded B-Variation 14

    1.3 Kurzweil and Henstock Vector Integrals 19

    1.3.1 Definitions 20

    1.3.2 Basic Properties 25

    1.3.3 Integration by Parts and Substitution Formulas 29

    1.3.4 The Fundamental Theorem of Calculus 36

    1.3.5 A Convergence Theorem 44

    Appendix 1.A: The McShane Integral 44

    2 The Kurzweil Integral 53
    Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Jaqueline G. Mesquita

    2.1 The Main Background 54

    2.1.1 Definition and Compatibility 54

    2.1.2 Special Integrals 56

    2.2 Basic Properties 57

    2.3 Notes on Kapitza Pendulum 67

    3 Measure Functional Differential Equations 71
    Everaldo M. Bonotto, Márcia Federson, Miguel V. S. Frasson, Rogelio Grau, and Jaqueline G. Mesquita

    3.1 Measure FDEs 74

    3.2 Impulsive Measure FDEs 76

    3.3 Functional Dynamic Equations on Time Scales 86

    3.3.1 Fundamentals of Time Scales 87

    3.3.2 The Perron ¿-integral 89

    3.3.3 Perron ¿-integrals and Perron-Stieltjes integrals 90

    3.3.4 MDEs and Dynamic Equations on Time Scales 98

    3.3.5 Relations with Measure FDEs 99

    3.3.6 Impulsive Functional Dynamic Equations on Time Scales 104

    3.4 Averaging Methods 106

    3.4.1 Periodic Averaging 107

    3.4.2 Nonperiodic Averaging 118

    3.5 Continuous Dependence on Time Scales 135

    4 Generalized Ordinary Differential Equations 145
    Everaldo M. Bonotto, Márcia Federson, and Jaqueline G. Mesquita

    4.1 Fundamental Properties 146

    4.2 Relations with Measure Differential Equations 153

    4.3 Relations with Measure FDEs 160

    5 Basic Properties of Solutions 173
    Everaldo M. Bonotto, Márcia Federson, Luciene P. Gimenes (in memorian), Rogelio Grau, Jaqueline G. Mesquita, and Eduard Toon

    5.1 Local Existence and Uniqueness of Solutions 174

    5.1.1 Applications to Other Equations 178

    5.2 Prolongation and Maximal Solutions 181

    5.2.1 Applications to MDEs 191

    5.2.2 Applications to Dynamic Equations on Time Scales 197

    6 Linear Generalized Ordinary Differential Equations 205
    Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Miguel V. S. Frasson

    6.1 The Fundamental Operator 207

    6.2 A Variation-of-Constants Formula 209

    6.3 Linear Measure FDEs 216

    6.4 A Nonlinear Variation-of-Constants Formula for Measure FDEs 220

    7 Continuous Dependence on Parameters 225
    Suzete M. Afonso, Everaldo M. Bonotto, Márcia Federson, and Jaqueline G. Mesquita

    7.1 Basic Theory for Generalized ODEs 226

    7.2 Applications to Measure FDEs 236

    8 StabilityTheory 241
    Suzete M. Afonso, Fernanda Andrade da Silva, Everaldo M. Bonotto, Márcia Federson, Luciene P. Gimenes (in memorian), Rogelio Grau, Jaqueline G. Mesquita, and Eduard Toon

    8.1 Variational Stability for Generalized ODEs 244

    8.1.1 Direct Method of Lyapunov 246

    8.1.2 Converse Lyapunov Theorems 247

    8.2 Lyapunov Stability for Generalized ODEs 256

    8.2.1 Direct Method of Lyapunov 257

    8.3 Lyapunov Stability for MDEs 261

    8.3.1 Direct Method of Lyapunov 263

    8.4 Lyapunov Stability for Dynamic Equations on Time Scales 265

    8.4.1 Direct Method of Lyapunov 267

    8.5 Regular Stability for Generalized ODEs 272

    8.5.1 Direct Method of Lyapunov 275

    8.5.2 Converse Lyapunov Theorem 282

    9 Periodicity 295
    Marielle Ap. Silva, Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Maria Carolina Mesquita

    9.1 Periodic Solutions and Floquet's Theorem 297

    9.1.1 Linear Differential Systems with Impulses 303

    9.2 (¿,T)-Periodic Solutions 307

    9.2.1 An Application to MDEs 313

    10 Averaging Principles 317
    Márcia Federson and Jaqueline G. Mesquita

    10.1 Periodic Averaging Principles 320

    10.1.1 An Application to IDEs 325

    10.2 Nonperiodic Averaging Principles 330

    11 Boundedness of Solutions 341
    Suzete M. Afonso, Fernanda Andrade da Silva, Everaldo M. Bonotto, Márcia Federson, Rogelio Grau, Jaqueline G. Mesquita, and Eduard Toon 11.1 Bounded Solutions and Lyapunov Functionals 342

    11.2 An Application to MDEs 352

    11.2.1 An Example 356

    12 Control Theory 361
    Fernanda Andrade da Silva, Márcia Federson, and Eduard Toon

    12.1 Controllability and Observability 362

    12.2 Applications to ODEs 365

    13 Dichotomies 369
    Everaldo M. Bonotto and Márcia Federson

    13.1 Basic Theory for Generalized ODEs 370

    13.2 Boundedness and Dichotomies 381

    13.3 Applications to MDEs 391

    13.4 Applications to IDEs 400

    14 Topological Dynamics 407
    Suzete M. Afonso, Marielle Ap. Silva, Everaldo M. Bonotto, and Márcia Federson

    14.1 The Compactness of the Class F0(¿,h) 408

    14.2 Existence of a Local Semidynamical System 411

    14.3 Existence of an Impulsive Semidynamical System 418

    14.4 LaSalle's Invariance Principle 423

    14.5 Recursive Properties 425

    15 Applications to Functional Differential Equations of Neutral Type 429
    Fernando G. Andrade, Miguel V. S. Frasson, and Patricia H. Tacuri

    15.1 Drops of History 429

    15.2 FDEs of Neutral Type with Finite Delay 435

    References 455

    List of Symbols 471

    Index 473