Solution sets for differential equations and inclusions:
Gespeichert in:
Beteiligte Personen: | , , |
---|---|
Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2013
|
Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
18 |
Schlagwörter: | |
Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=4097601&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025718442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Beschreibung: | Literaturverz. S. [415] - 450 |
Umfang: | XIX, 453 S. 25 cm |
ISBN: | 3110293447 9783110293449 |
Internformat
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100 | 1 | |a Djebali, Smaïl |e Verfasser |4 aut | |
245 | 1 | 0 | |a Solution sets for differential equations and inclusions |c Smaïl Djebali ; Lech Górniewicz ; Abdelghani Ouahab |
264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2013 | |
300 | |a XIX, 453 S. |c 25 cm | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
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490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v 18 | |
500 | |a Literaturverz. S. [415] - 450 | ||
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700 | 1 | |a Ouahab, Abdelghani |e Verfasser |4 aut | |
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Datensatz im Suchindex
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---|---|
adam_text | IMAGE 1
CONTENTS
PREFACE VII
NOTATIONS XI
1 TOPOLOGICAL STRUCTURE O F FIXED POINT SETS 1
1.1 CASE O F SINGLE-VALUED MAPPINGS 1
1.1.1 FUNDAMENTAL FIXED POINT THEOREMS 1
1.1.1.1 BANACH S FIXED POINT THEOREM 1
1.1.1.2 BROUWER S FIXED POINT THEOREM 5
1.1.1.3 SCHAUDER S FIXED POINT THEOREM 7
1.1.2 APPROXIMATION THEOREMS 11
1.1.3 BROWDER-GUPTA THEOREMS 13
1.1.4 ACYCLICITY O F THE SOLUTION SETS O F OPERATOR EQUATIONS 20
1.1.5 NONEXPANSIVE MAPS 23
1.1.5.1 EXISTENCE THEORY 23
1.1.5.2 SOLUTION SETS 26
1.2 THE CASE O F MULTI-VALUED MAPPINGS 27
1.2.1 APPROXIMATION OF MULTI-VALUED MAPS 27
1.2.2 FIXED POINT THEOREMS 30
1.2.3 MULTI-VALUED CONTRACTIONS 33
1.2.4 FIXED POINT SETS O F MULTI-VALUED CONTRACTIONS 35
1.2.5 FIXED POINT SETS O F MULTI-VALUED NONEXPANSIVE MAPS 38
1.2.6 FIXED POINT SETS O F MULTI-VALUED CONDENSING MAPS 39
1.2.6.1 MEASURE O F NONCOMPACTNESS 39
1.2.6.2 CONDENSING MAPS 43
1.3 ADMISSIBLE MAPS 4 4
1.3.1 GENERALITIES 44
1.3.2 FIXED POINT THEOREMS FOR ADMISSIBLE MULTI-VALUED MAPS 53 1.3.3 THE
GENERAL BROUWER FIXED POINT THEOREM 58
1.3.4 BROWDER-GUPTA TYPE RESULTS FOR ADMISSIBLE MAPPINGS 60
1.3.5 TOPOLOGICAL DIMENSIONS O F SOLUTION SETS 62
HTTP://D-NB.INFO/1024944476
IMAGE 2
XVI CONTENTS
1.4 TOPOLOGICAL STRUCTURE O F FIXED POINT SETS O F INVERSE LIMIT MAPS .
65 1.4.1 DEFINITION 65
1.4.2 BASIC PROPERTIES 66
1.4.3 MULTI-MAPS OF INVERSE SYSTEMS 67
2 EXISTENCE THEORY FOR DIFFERENTIAL EQUATIONS AND INCLUSIONS 72
2.1 FUNDAMENTAL THEOREMS 72
2.1.1 EXISTENCE AND UNIQUENESS RESULTS 7 2
2.1.2 PICARD-LINDELOF THEOREM 73
2.1.2.1 MAXIMAL SOLUTIONS 75
2.1.3 PEANO AND CARATHEODORY THEOREMS 77
2.1.3.1 PEANO THEOREM 77
2.2 THE EXTENDABILITY PROBLEM 79
2.2.1 GLOBAL EXISTENCE THEOREMS 79
2.2.2 EXISTENCE RESULTS ON NONCOMPACT INTERVALS 82
2.2.2.1 THE LIPSCHITZ CASE 82
2.2.2.2 THE LIPSCHITZ-NAGUMO CASE 83
2.2.2.3 THE NAGUMO CASE 86
2.2.3 A BOUNDARY VALUE PROBLEM ON THE HALF-LINE 88
2.3 THE CASE O F DIFFERENTIAL INCLUSIONS 94
2.3.1 INITIAL VALUE PROBLEMS 94
2.3.1.1 A NAGUMO TYPE NONLINEARITY 94
2.3.1.2 A LIPSCHITZ NONCONVEX NONLINEARITY 97
2.3.2 BOUNDARY VALUE PROBLEMS 99
2.3.2.1 THE CONVEX CASE 100
2.3.2.2 THE NONCONVEX CASE 103
3 SOLUTION SETS FOR DIFFERENTIAL EQUATIONS AND INCLUSIONS 105
3.1 GENERAL RESULTS 105
3.1.1 KNESER-HUKUHARA THEOREM 105
3.1.2 PROBLEMS ON BOUNDED INTERVALS 108
3.1.3 PROBLEMS ON UNBOUNDED INTERVALS 109
3.1.4 SECOND-ORDER DIFFERENTIAL EQUATIONS I L L
3.1.5 ABSTRACT VOLTERRA EQUATIONS 113
3.1.6 ARONSZAJN TYPE RESULTS FOR DIFFERENTIAL INCLUSIONS 114
3.2 SECOND-ORDER DIFFERENTIAL INCLUSIONS 122
3.2.1 THE CONVEX CASE 122
3.2.2 THE NONCONVEX CASE 127
3.2.3 SOLUTION SETS 130
IMAGE 3
CONTENTS XVII
3.3 HIGHER-ORDER DIFFERENTIAL INCLUSIONS 134
3.4 NEUTRAL DIFFERENTIAL INCLUSIONS 135
3.4.1 THE CONVEX CASE 136
3.4.2 THE NONCONVEX CASE 142
3.4.3 SOLUTIONS SETS 146
3.5 NONLOCAL PROBLEMS 146
3.5.1 MAIN RESULTS 147
3.5.2 A VIABILITY PROBLEM 149
3.6 HYPERBOLIC DIFFERENTIAL INCLUSIONS 154
3.6.1 EXISTENCE RESULTS . 155
3.6.1.1 THE CONVEX CASE 155
3.6.1.2 THE NONCONVEX CASE 159
3.6.2 SOLUTION SETS 160
4 IMPULSIVE DIFFERENTIAL INCLUSIONS: EXISTENCE AND SOLUTION SETS 163
4.1 MOTIVATION 163
4.1.1 ECOLOGICAL MODEL WITH IMPULSIVE CONTROL STRATEGY 163
4.1.2 LESLIE PREDATOR-PREY SYSTEM 164
4.1.3 PULSE VACCINATION MODEL 165
4.2 SEMI-LINEAR IMPULSIVE DIFFERENTIAL INCLUSIONS 166
4.2.1 EXISTENCE RESULTS 166
4.2.1.1 THE CONVEX CASE 167
4.2.1.2 THE NONCONVEX CASE 181
4.2.2 STRUCTURE O F SOLUTION SETS 186
4.3 A PERIODIC PROBLEM 197
4.3.1 EXISTENCE RESULTS: 1 E P{T(B)) 198
4.3.2 THE CONVEX CASE: A DIRECT APPROACH 199
4.3.3 THE CONVEX CASE: AN MNC APPROACH 207
4.3.4 THE NONCONVEX CASE 212
4.3.5 THE PARAMETER-DEPENDANT CASE 215
4.3.5.1 THE CONVEX CASE 215
4.3.5.2 THE NONCONVEX CASE 217
4.3.6 FILIPPOV S THEOREM 220
4.3.7 EXISTENCE O F SOLUTIONS: 1 $ P{T(B)) 230
4.3.7.1 A NONLINEAR ALTERNATIVE 230
4.3.7.2 A POINCARE TRANSLATION OPERATOR 233
4.3.7.3 THE MNC APPROACH 233
IMAGE 4
XV111
CONTENTS
4.4 IMPULSIVE FUNCTIONAL DIFFERENTIAL INCLUSIONS 236
4.4.1 INTRODUCTION 236
4.4.2 EXISTENCE RESULTS 237
4.4.3 STRUCTURE O F THE SOLUTION SET 246
4.5 IMPULSIVE DIFFERENTIAL INCLUSIONS ON THE HALF-LINE 250
4.5.1 EXISTENCE RESULTS AND COMPACTNESS O F SOLUTION SETS 250
4.5.1.1 THE CONVEX U.S.C. CASE 251
4.5.1.2 THE NONCONVEX LIPSCHITZ CASE 258
4.5.1.3 THE NONCONVEX L.S.C. CASE 262
4.5.2 TOPOLOGICAL STRUCTURE VIA THE PROJECTIVE LIMIT 265
4.5.2.1 THE NONCONVEX CASE 266
4.5.2.2 THE CONVEX CASE 271
4.5.2.3 THE TERMINAL PROBLEM 274
4.5.3 USING SOLUTION SETS TO PROVE EXISTENCE RESULTS 283
5 PRELIMINARY NOTIONS O F TOPOLOGY AND HOMOLOGY 288
5.1 RETRACTS, EXTENSION AND EMBEDDING PROPERTIES 288
5.2 ABSOLUTE RETRACTS 294
5.3 HOMOTOPICAL PROPERTIES O F SPACES 296
5.4 CECH HOMOLOGY (COHOMOLOGY) FUNCTOR 304
5.5 MAPS O F SPACES O F FINITE TYPE 306
5.6 CECH HOMOLOGY FUNCTOR WITH COMPACT CARRIERS 313
5.7 ACYCLIC SETS AND VIETORIS MAPS 315
5.8 HOMOLOGY O F OPEN SUBSETS O F EUCLIDEAN SPACES 319
5.9 LEFSCHETZ NUMBER 323
5.10 THE COINCIDENCE PROBLEM 330
6 BACKGROUND IN MULTI-VALUED ANALYSIS 337
6.1 CONTINUITY O F MULTI-VALUED MAPPINGS 339
6.1.1 BASIC NOTIONS 339
6.1.2 UPPER SEMI-CONTINUITY 341
6.1.2.1 GENERALITIES 341
6.1.2.2 E - 8 U.S.C. MAPPINGS 344
6.1.2.3 U.S.C. MAPS AND CLOSED GRAPHS 345
6.1.3 LOWER SEMI-CONTINUITY 346
6.1.3.1 GENERALITIES 346
6.1.3.2 S - S L.S.C. MAPPINGS 349
6.1.4 HAUSDORFF CONTINUITY 350
IMAGE 5
CONTENTS XIX
6.2 THE SELECTION PROBLEM 354
6.2.1 MICHAEL S SELECTION THEOREM 355
6.2.2 MICHAEL S FAMILY O F SUBSETS 358
6.2.3 A-SELECTIONABLE MAPPINGS 362
6.2.4 THE KURATOWSKI-RYLL-NARDZEWSKI SELECTION THEOREM 366 6.2.5 AUMANN
AND FILIPPOV THEOREMS 378
6.2.6 HAUSDORFF MEASURABLE MULTI-VALUED MAPS 382
6.2.7 PRODUCT-MEASURABILITY AND THE SCORZA-DRAGONI PROPERTY 383
6.3 DECOMPOSABLE SETS 390
6.3.1 THE BRESSAN-COLOMBO-FRYSZKOWSKI SELECTION THEOREM 390 6.3.2
DECOMPOSABILITY IN L L ( T , E ) 390
6.3.3 INTEGRATION O F MULTI-VALUED MAPS 392
6.3.4 NEMYTSKII OPERATORS 393
APPENDIX 399
A. 1 AXIOMS O F THE CECH HOMOLOGY THEORY 399
A.2 THE BOCHNER INTEGRAL 400
A.3 ABSOLUTELY CONTINUOUS FUNCTIONS 403
A.4 COMPACTNESS CRITERIA IN C([A, B], E), Q,([0, OO), E ) , AND P C ( [
A , B ] , E ) 405
A.5 WEAK-COMPACTNESS IN L 1 408
A.6 PROPER MAPS AND VECTOR FIELDS 410
A.7 FUNDAMENTAL THEOREMS IN FUNCTIONAL ANALYSIS 411
A.8 CO -SEMIGROUPS 412
REFERENCES 415
INDEX 451
|
any_adam_object | 1 |
author | Djebali, Smaïl Górniewicz, Lech Ouahab, Abdelghani |
author_facet | Djebali, Smaïl Górniewicz, Lech Ouahab, Abdelghani |
author_role | aut aut aut |
author_sort | Djebali, Smaïl |
author_variant | s d sd l g lg a o ao |
building | Verbundindex |
bvnumber | BV040738460 |
classification_rvk | SK 520 |
ctrlnum | (OCoLC)820627203 (DE-599)DNB1024944476 |
dewey-full | 515.35 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515.35 |
dewey-search | 515.35 |
dewey-sort | 3515.35 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV040738460 |
illustrated | Not Illustrated |
indexdate | 2024-12-20T16:24:39Z |
institution | BVB |
isbn | 3110293447 9783110293449 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025718442 |
oclc_num | 820627203 |
open_access_boolean | |
owner | DE-19 DE-BY-UBM DE-634 DE-824 DE-20 |
owner_facet | DE-19 DE-BY-UBM DE-634 DE-824 DE-20 |
physical | XIX, 453 S. 25 cm |
publishDate | 2013 |
publishDateSearch | 2013 |
publishDateSort | 2013 |
publisher | de Gruyter |
record_format | marc |
series | De Gruyter series in nonlinear analysis and applications |
series2 | De Gruyter series in nonlinear analysis and applications |
spellingShingle | Djebali, Smaïl Górniewicz, Lech Ouahab, Abdelghani Solution sets for differential equations and inclusions De Gruyter series in nonlinear analysis and applications Lösung Mathematik (DE-588)4120678-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Differentialinklusion (DE-588)4149777-6 gnd Fixpunkt (DE-588)4154496-1 gnd |
subject_GND | (DE-588)4120678-2 (DE-588)4012249-9 (DE-588)4149777-6 (DE-588)4154496-1 |
title | Solution sets for differential equations and inclusions |
title_auth | Solution sets for differential equations and inclusions |
title_exact_search | Solution sets for differential equations and inclusions |
title_full | Solution sets for differential equations and inclusions Smaïl Djebali ; Lech Górniewicz ; Abdelghani Ouahab |
title_fullStr | Solution sets for differential equations and inclusions Smaïl Djebali ; Lech Górniewicz ; Abdelghani Ouahab |
title_full_unstemmed | Solution sets for differential equations and inclusions Smaïl Djebali ; Lech Górniewicz ; Abdelghani Ouahab |
title_short | Solution sets for differential equations and inclusions |
title_sort | solution sets for differential equations and inclusions |
topic | Lösung Mathematik (DE-588)4120678-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Differentialinklusion (DE-588)4149777-6 gnd Fixpunkt (DE-588)4154496-1 gnd |
topic_facet | Lösung Mathematik Differentialgleichung Differentialinklusion Fixpunkt |
url | http://deposit.dnb.de/cgi-bin/dokserv?id=4097601&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025718442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV005530011 |
work_keys_str_mv | AT djebalismail solutionsetsfordifferentialequationsandinclusions AT gorniewiczlech solutionsetsfordifferentialequationsandinclusions AT ouahababdelghani solutionsetsfordifferentialequationsandinclusions |