Volterra integral and differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Elsevier
2005
|
| Edition: | 2. ed. |
| Series: | Mathematics in science and engineering
202 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 353 S. |
| ISBN: | 0444517863 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | VOLTERRA INTEGRAL AND DIFFERENTIAL EQUATIONS SECOND EDITION T.A. BURTON
DEPARTMENT OF MATHEMATICS SOUTHERN ILLINOIS UNIVERSITY CARBONDALE,
ILLINOIS USA 2005 ELSEVIER AMSTERDAM - BOSTON - HEIDELBERG - LONDON -
NEW YORK - OXFORD PARIS - SAN DIEGO - SAN FRANCISCO - SINGAPORE - SYDNEY
- TOKYO CONTENTS PREFACE V PREFACE TO THE SECOND EDITION VII 0
INTRODUCTION AND OVERVIEW 1 0.1 STATEMENT OF PURPOSE 1 0.2 AN OVERVIEW 2
1 THE GENERAL PROBLEMS 5 1.1 INTRODUCTION 5 1.2 RELATIONS BETWEEN
DIFFERENTIAL AND INTEGRAL EQUATIONS ... 7 1.3 A GLANCE AT INITIAL
CONDITIONS AND EXISTENCE 13 1.4 BUILDING THE INTUITION 15 1.5 REDUCIBLE
EQUATIONS 20 2 LINEAR EQUATIONS 23 2.1 EXISTENCE THEORY 23 2.2 LINEAR
PROPERTIES 27 2.3 CONVOLUTION AND THE LAPLACE TRANSFORM 30 2.4 STABILITY
36 2.5 LIAPUNOV FUNCTIONAL AND SMALL KERNELS 40 2.6 UNIFORM ASYMPTOTIC
STABILITY 51 2.7 REDUCIBLE EQUATIONS REVISITED 65 3 EXISTENCE PROPERTIES
69 3.1 DEFINITIONS, BACKGROUND, AND REVIEW 69 3.2 EXISTENCE AND
UNIQUENESS 76 3.3 CONTINUATION OF SOLUTIONS 82 3.4 CONTINUITY OF
SOLUTIONS 95 X CONTENTS 4 HISTORY, EXAMPLES, AND MOTIVATION 103 4.0
INTRODUCTION 103 4.1 VOLTERRA AND MATHEMATICAL BIOLOGY 104 4.2 RENEWAL
THEORY 120 4.3 EXAMPLES 123 5 INSTABILITY, STABILITY, AND PERTURBATIONS
133 5.1 THE MATRIX A T B + BA 133 5.2 THE SCALAR EQUATION 142 5.3 THE
VECTOR EQUATION 154 5.4 COMPLETE INSTABILITY 163 5.5 NON-EXPONENTIAL
DECAY 167 6 STABILITY AND BOUNDEDNESS 171 6.1 STABILITY THEORY FOR
ORDINARY DIFFERENTIAL EQUATIONS .... 171 6.2 CONSTRUCTION OF LIAPUNOV
FUNCTIONS 183 6.3 A FIRST INTEGRAL LIAPUNOV FUNCTIONAL 191 6.4
NONLINEARITIES AND AN ANNULUS ARGUMENT 198 6.5 A FUNCTIONAL IN THE
UNSTABLE CASE 211 7 THE RESOLVENT 217 7.1 GENERAL THEORY 217 7.2 A
FLOQUET THEORY 223 7.3 UAS AND INTEGRABILITY OF THE RESOLVENT 233 8
FUNCTIONAL DIFFERENTIAL EQUATIONS 243 8.0 INTRODUCTION 243 8.1 EXISTENCE
AND UNIQUENESS 244 8.2 ASYMPTOTIC STABILITY 254 8.3 EQUATIONS WITH
BOUNDED DELAY 264 8.4 BOUNDEDNESS WITH UNBOUNDED DELAY 293 8.5 LIMIT
SETS 308 8.6 PERIODIC SOLUTIONS 316 8.7 LIMIT SETS AND UNBOUNDED DELAYS
330 8.8 LIAPUNOV THEORY FOR INTEGRAL EQUATIONS 339 REFERENCES 340 AUTHOR
INDEX 349 SUBJECT INDEX 351
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV019802913 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:06:28Z |
| institution | BVB |
| isbn | 0444517863 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013128462 |
| oclc_num | 57722494 |
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| owner_facet | DE-91G DE-BY-TUM DE-824 |
| physical | X, 353 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Elsevier |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Burton, Theodore A. 1935- Verfasser (DE-588)143771280 aut Volterra integral and differential equations T. A. Burton 2. ed. New York [u.a.] Elsevier 2005 X, 353 S. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 202 Integro-differential equations Volterra equations Integrodifferentialgleichung (DE-588)4161939-0 gnd rswk-swf Volterra-Gleichungen (DE-588)4137459-9 gnd rswk-swf Volterra-Integralgleichung (DE-588)4234593-5 gnd rswk-swf Volterra-Gleichungen (DE-588)4137459-9 s DE-604 Integrodifferentialgleichung (DE-588)4161939-0 s Volterra-Integralgleichung (DE-588)4234593-5 s Mathematics in science and engineering 202 (DE-604)BV000001196 202 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013128462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burton, Theodore A. 1935- Volterra integral and differential equations Mathematics in science and engineering Integro-differential equations Volterra equations Integrodifferentialgleichung (DE-588)4161939-0 gnd Volterra-Gleichungen (DE-588)4137459-9 gnd Volterra-Integralgleichung (DE-588)4234593-5 gnd |
| subject_GND | (DE-588)4161939-0 (DE-588)4137459-9 (DE-588)4234593-5 |
| title | Volterra integral and differential equations |
| title_auth | Volterra integral and differential equations |
| title_exact_search | Volterra integral and differential equations |
| title_full | Volterra integral and differential equations T. A. Burton |
| title_fullStr | Volterra integral and differential equations T. A. Burton |
| title_full_unstemmed | Volterra integral and differential equations T. A. Burton |
| title_short | Volterra integral and differential equations |
| title_sort | volterra integral and differential equations |
| topic | Integro-differential equations Volterra equations Integrodifferentialgleichung (DE-588)4161939-0 gnd Volterra-Gleichungen (DE-588)4137459-9 gnd Volterra-Integralgleichung (DE-588)4234593-5 gnd |
| topic_facet | Integro-differential equations Volterra equations Integrodifferentialgleichung Volterra-Gleichungen Volterra-Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013128462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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