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CITU |
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20241113141507.0 |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119654933 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119655022 |
| Qualifying information |
(electronic bk. : oBook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1119655021 |
| Qualifying information |
(electronic bk. : oBook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781119654933 |
| Qualifying information |
(print) |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1002/9781119655022 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)1269499134 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
DG1 |
| Language of cataloging |
eng |
| Description conventions |
rda |
| -- |
pn |
| Transcribing agency |
DG1 |
| Modifying agency |
OCLCO |
| -- |
UKAHL |
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OCLCF |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA372 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515/.352 |
| Edition number |
23 |
| 245 00 - TITLE STATEMENT |
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| Title |
Generalized ordinary differential equations in abstract spaces and applications / |
| Statement of responsibility, etc |
edited by Everaldo M. Bonotto, Marcia Federson, Jacqueline G. Mesquita. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Hoboken, NJ : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
2021. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
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rdacontent. |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia. |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier. |
| 340 ## - PHYSICAL MEDIUM |
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| Source |
rdacc |
| Authority record control number or standard number |
http://rdaregistry.info/termList/RDAColourContent/1003. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - CONTENTS |
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| Formatted contents note |
Table of Contents<br/>List of Contributors xi<br/><br/>Foreword xiii<br/><br/>Preface xvii<br/><br/>1 Preliminaries 1<br/>Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, Jaqueline G. Mesquita, and Eduard Toon<br/><br/>1.1 Regulated Functions 2<br/><br/>1.1.1 Basic Properties 2<br/><br/>1.1.2 Equiregulated Sets 7<br/><br/>1.1.3 Uniform Convergence 9<br/><br/>1.1.4 Relatively Compact Sets 11<br/><br/>1.2 Functions of Bounded B-Variation 14<br/><br/>1.3 Kurzweil and Henstock Vector Integrals 19<br/><br/>1.3.1 Definitions 20<br/><br/>1.3.2 Basic Properties 25<br/><br/>1.3.3 Integration by Parts and Substitution Formulas 29<br/><br/>1.3.4 The Fundamental Theorem of Calculus 36<br/><br/>1.3.5 A Convergence Theorem 44<br/><br/>Appendix 1.A: The McShane Integral 44<br/><br/>2 The Kurzweil Integral 53<br/>Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Jaqueline G. Mesquita<br/><br/>2.1 The Main Background 54<br/><br/>2.1.1 Definition and Compatibility 54<br/><br/>2.1.2 Special Integrals 56<br/><br/>2.2 Basic Properties 57<br/><br/>2.3 Notes on Kapitza Pendulum 67<br/><br/>3 Measure Functional Differential Equations 71<br/>Everaldo M. Bonotto, Márcia Federson, Miguel V. S. Frasson, Rogelio Grau, and Jaqueline G. Mesquita<br/><br/>3.1 Measure FDEs 74<br/><br/>3.2 Impulsive Measure FDEs 76<br/><br/>3.3 Functional Dynamic Equations on Time Scales 86<br/><br/>3.3.1 Fundamentals of Time Scales 87<br/><br/>3.3.2 The Perron Δ-integral 89<br/><br/>3.3.3 Perron Δ-integrals and Perron–Stieltjes integrals 90<br/><br/>3.3.4 MDEs and Dynamic Equations on Time Scales 98<br/><br/>3.3.5 Relations with Measure FDEs 99<br/><br/>3.3.6 Impulsive Functional Dynamic Equations on Time Scales 104<br/><br/>3.4 Averaging Methods 106<br/><br/>3.4.1 Periodic Averaging 107<br/><br/>3.4.2 Nonperiodic Averaging 118<br/><br/>3.5 Continuous Dependence on Time Scales 135<br/><br/>4 Generalized Ordinary Differential Equations 145<br/>Everaldo M. Bonotto, Márcia Federson, and Jaqueline G. Mesquita<br/><br/>4.1 Fundamental Properties 146<br/><br/>4.2 Relations with Measure Differential Equations 153<br/><br/>4.3 Relations with Measure FDEs 160<br/><br/>5 Basic Properties of Solutions 173<br/>Everaldo M. Bonotto, Márcia Federson, Luciene P. Gimenes (in memorian), Rogelio Grau, Jaqueline G. Mesquita, and Eduard Toon<br/><br/>5.1 Local Existence and Uniqueness of Solutions 174<br/><br/>5.1.1 Applications to Other Equations 178<br/><br/>5.2 Prolongation and Maximal Solutions 181<br/><br/>5.2.1 Applications to MDEs 191<br/><br/>5.2.2 Applications to Dynamic Equations on Time Scales 197<br/><br/>6 Linear Generalized Ordinary Differential Equations 205<br/>Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Miguel V. S. Frasson<br/><br/>6.1 The Fundamental Operator 207<br/><br/>6.2 A Variation-of-Constants Formula 209<br/><br/>6.3 Linear Measure FDEs 216<br/><br/>6.4 A Nonlinear Variation-of-Constants Formula for Measure FDEs 220<br/><br/>7 Continuous Dependence on Parameters 225<br/>Suzete M. Afonso, Everaldo M. Bonotto, Márcia Federson, and Jaqueline G. Mesquita<br/><br/>7.1 Basic Theory for Generalized ODEs 226<br/><br/>7.2 Applications to Measure FDEs 236<br/><br/>8 StabilityTheory 241<br/>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<br/><br/>8.1 Variational Stability for Generalized ODEs 244<br/><br/>8.1.1 Direct Method of Lyapunov 246<br/><br/>8.1.2 Converse Lyapunov Theorems 247<br/><br/>8.2 Lyapunov Stability for Generalized ODEs 256<br/><br/>8.2.1 Direct Method of Lyapunov 257<br/><br/>8.3 Lyapunov Stability for MDEs 261<br/><br/>8.3.1 Direct Method of Lyapunov 263<br/><br/>8.4 Lyapunov Stability for Dynamic Equations on Time Scales 265<br/><br/>8.4.1 Direct Method of Lyapunov 267<br/><br/>8.5 Regular Stability for Generalized ODEs 272<br/><br/>8.5.1 Direct Method of Lyapunov 275<br/><br/>8.5.2 Converse Lyapunov Theorem 282<br/><br/>9 Periodicity 295<br/>Marielle Ap. Silva, Everaldo M. Bonotto, Rodolfo Collegari, Márcia Federson, and Maria Carolina Mesquita<br/><br/>9.1 Periodic Solutions and Floquet’s Theorem 297<br/><br/>9.1.1 Linear Differential Systems with Impulses 303<br/><br/>9.2 (θ,T)-Periodic Solutions 307<br/><br/>9.2.1 An Application to MDEs 313<br/><br/>10 Averaging Principles 317<br/>Márcia Federson and Jaqueline G. Mesquita<br/><br/>10.1 Periodic Averaging Principles 320<br/><br/>10.1.1 An Application to IDEs 325<br/><br/>10.2 Nonperiodic Averaging Principles 330<br/><br/>11 Boundedness of Solutions 341<br/>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<br/><br/>11.2 An Application to MDEs 352<br/><br/>11.2.1 An Example 356<br/><br/>12 Control Theory 361<br/>Fernanda Andrade da Silva, Márcia Federson, and Eduard Toon<br/><br/>12.1 Controllability and Observability 362<br/><br/>12.2 Applications to ODEs 365<br/><br/>13 Dichotomies 369<br/>Everaldo M. Bonotto and Márcia Federson<br/><br/>13.1 Basic Theory for Generalized ODEs 370<br/><br/>13.2 Boundedness and Dichotomies 381<br/><br/>13.3 Applications to MDEs 391<br/><br/>13.4 Applications to IDEs 400<br/><br/>14 Topological Dynamics 407<br/>Suzete M. Afonso, Marielle Ap. Silva, Everaldo M. Bonotto, and Márcia Federson<br/><br/>14.1 The Compactness of the Class F0(Ω,h) 408<br/><br/>14.2 Existence of a Local Semidynamical System 411<br/><br/>14.3 Existence of an Impulsive Semidynamical System 418<br/><br/>14.4 LaSalle’s Invariance Principle 423<br/><br/>14.5 Recursive Properties 425<br/><br/>15 Applications to Functional Differential Equations of Neutral Type 429<br/>Fernando G. Andrade, Miguel V. S. Frasson, and Patricia H. Tacuri<br/><br/>15.1 Drops of History 429<br/><br/>15.2 FDEs of Neutral Type with Finite Delay 435<br/><br/>References 455<br/><br/>List of Symbols 471<br/><br/>Index 473 |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
|---|
| Biographical or historical note |
About the Author<br/>Everaldo M. Bonotto, PhD, is Associate Professor in the Department of Applied Mathematics and Statistics, at ICMC-Universidade de São Paulo, São Carlos, SP, Brazil.<br/><br/>Márcia Federson, PhD, is Full Professor in the Department of Mathematics at ICMC-Universidade de São Paulo, São Carlos, SP, Brazil.<br/><br/>Jaqueline G. Mesquita, PhD, is Assistant Professor at Department of Mathematics at the University of Brasília, Brasília, DF, Brazil. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations. |
| Authority record control number |
http://id.loc.gov/authorities/subjects/sh85037890. |
| 655 #4 - INDEX TERM--GENRE/FORM |
|---|
| Genre/form data or focus term |
Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Bonotto, Everaldo M., |
| Relator term |
editor. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Federson, Marcia, |
| Relator term |
editor. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Mesquita, Jacqueline G., |
| Relator term |
editor. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119655022 |
| Link text |
Full text is available at Wiley Online Library Click here to view |
| 942 ## - ADDED ENTRY ELEMENTS |
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| Source of classification or shelving scheme |
|
| Item type |
EBOOK |