Impulsive differential inclusions: a fixed point approach
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2013
|
| Series: | De Gruyter series in nonlinear analysis and applications
20 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [369] - 397 |
| Physical Description: | X, 400 S. 25 cm |
| ISBN: | 9783110293616 |
Staff View
MARC
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| 245 | 1 | 0 | |a Impulsive differential inclusions |b a fixed point approach |c John R. Graef ; Johnny Henderson ; Abdelghani Ouahab |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2013 | |
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Record in the Search Index
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IMAGE 1
CONTENTS
NOTATIONS XI
1 INTRODUCTION AND MOTIVATIONS 1
1.1 INTRODUCTION 1
1.2 MOTIVATIONAL MODELS 8
1.2.1 KRUGER-THIEMER MODEL 8
1.2.2 LOTKA-VOLTERRA MODEL 8
1.2.3 PULSE VACCINATION MODEL 9
1.2.4 MANAGEMENT MODEL 9
1.2.5 SOME EXAMPLES IN ECONOMICS AND BIOMATHEMATICS 10
2 PRELIMINARIES 11
2.1 SOME DEFINITIONS 11
2.2 SOME PROPERTIES IN FRECHET SPACES 12
2.3 SOME PROPERTIES O F SET-VALUED MAPS 13
2.3.1 HAUSDORFF METRIC TOPOLOGY 15
2.3.2 VIETORIS TOPOLOGY 18
2.3.3 CONTINUITY CONCEPTS AND THEIR RELATIONS 20
2.3.4 SELECTION FUNCTIONS AND SELECTION THEOREMS 28
2.3.5 HAUSDORFF CONTINUITY 30
2.3.6 MEASURABLE MULTIFUNCTIONS 32
2.3.7 DECOMPOSABLE SELECTION 35
2.4 FIXED POINT THEOREMS 36
2.5 MEASURES O F NONCOMPACTNESS: MNC 37
2.6 SEMIGROUPS 40
2.6.1 Q-SEMIGROUPS 40
2.6.2 INTEGRATED SEMIGROUPS 42
2.6.3 EXAMPLES 44
2.7 EXTRAPOLATION SPACES 45
3 FDES WITH INFINITE DELAY 47
3.1 FIRST ORDER FDES 47
3.1.1 EXAMPLES O F PHASE SPACES 48
HTTP://D-NB.INFO/1032800860
IMAGE 2
VIII CONTENTS
3.1.2 EXISTENCE AND UNIQUENESS ON COMPACT INTERVALS 50
3.1.3 AN EXAMPLE 57
3.2 FDES WITH MULTIPLE DELAYS 58
3.2.1 EXISTENCE AND UNIQUENESS RESULT ON A COMPACT INTERVAL 58 3.2.2
GLOBAL EXISTENCE AND UNIQUENESS RESULT 65
3.3 STABILITY 66
3.3.1 STABILITY RESULT 67
3.4 SECOND ORDER IMPULSIVE FDES 69
3.4.1 EXISTENCE AND UNIQUENESS RESULTS 71
3.5 GLOBAL EXISTENCE AND UNIQUENESS RESULT 76
3.5.1 UNIQUENESS RESULT 77
3.5.2 EXAMPLE 82
3.5.3 STABILITY 83
4 BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS 86
4.1 INTRODUCTION 86
4.1.1 EXISTENCE RESULT 87
4.1.2 UNIQUENESS RESULT 92
4.1.3 EXAMPLE 96
5 DIFFERENTIAL INCLUSIONS 98
5.1 INTRODUCTION 98
5.1.1 FILIPPOV'S THEOREM 98
5.1.2 RELAXATION THEOREM I L L
5.2 FUNCTIONAL DIFFERENTIAL INCLUSIONS 113
5.2.1 FILIPPOV'S THEOREM FOR FDIS 114
5.2.2 SOME PROPERTIES O F SOLUTION SETS 123
5.3 UPPER SEMICONTINUITY WITHOUT CONVEXITY 125
5.3.1 NONCONVEX THEOREM AND UPPER SEMICONTINUITY 126
5.3.2 AN APPLICATION 130
5.4 INCLUSIONS WITH DISSIPATIVE RIGHT HAND SIDE 131
5.4.1 EXISTENCE AND UNIQUENESS RESULT 131
5.5 DIRECTIONALLY CONTINUOUS SELECTION AND IDIS 136
5.5.1 DIRECTIONAL CONTINUITY 136
6 DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY 1 40
6.1 EXISTENCE RESULTS 140
6.2 BOUNDARY DIFFERENTIAL INCLUSIONS 150
IMAGE 3
CONTENTS IX
7 IMPULSIVE FDES WITH VARIABLE TIMES 1 54
7.1 INTRODUCTION 154
7.1.1 EXISTENCE RESULTS 154
7.1.2 NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS 155
7.2 IMPULSIVE HYPERBOLIC DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY . .
. . 156
7.3 EXISTENCE RESULTS 157
7.3.1 PHASE SPACES 157
7.3.2 THE NONCONVEX CASE 168
8 NEUTRAL DIFFERENTIAL INCLUSIONS 171
8.1 FILIPPOV'S THEOREM 171
8.2 THE RELAXED PROBLEM 182
8.2.1 EXISTENCE AND COMPACTNESS RESULT: AN MNC APPROACH 189
9 TOPOLOGY AND GEOMETRY O F SOLUTION SETS 199
9.1 BACKGROUND IN GEOMETRIC TOPOLOGY 199
9.2 ARONSZAJN TYPE RESULTS 201
9.2.1 SOLUTION SETS FOR IMPULSIVE DIFFERENTIAL EQUATIONS 206
9.3 SOLUTION SETS O F DIFFERENTIAL INCLUSIONS 208
9.4 CT-SELECTIONABLE MULTIVALUED MAPS 208
9.4.1 CONTRACTIBLE AND /^-CONTRACTIBLE 212
9.4.2 RG-SETS 218
9.5 IMPULSIVE DIS ON PROXIMATE RETRACTS 219
9.5.1 VIABLE SOLUTION 220
9.6 PERIODIC PROBLEMS 226
9.6.1 POINCARE TRANSLATION OPERATOR 226
9.6.2 EXISTENCE RESULT 227
9.7 SOLUTION SET FOR NONCONVEX CASE 231
9.7.1 CONTINUOUS SELECTION AND AR O F SOLUTION SETS 232
9.8 THE TERMINAL PROBLEM 245
9.8.1 EXISTENCE AND SOLUTION SET 245
10 IMPULSIVE SEMILINEAR DIFFERENTIAL INCLUSIONS 254
10.1 NONDENSELY DEFINED OPERATORS 254
10.2 INTEGRAL SOLUTIONS 255
10.3 EXACT CONTROLLABILITY 267
10.3.1 CONTROLLABILITY O F IMPULSIVE FDIS 267
10.3.2 CONTROLLABILITY O F IMPULSIVE NEUTRAL FDIS 276
IMAGE 4
X CONTENTS
10.4 CONTROLLABILITY IN EXTRAPOLATION SPACES 282
10.5 SECOND ORDER IMPULSIVE SEMILINEAR FDIS 290
10.5.1 MILD SOLUTIONS 291
10.5.2 FILIPPOV'S THEOREM 292
10.5.3 FILIPPOV-WAZEWSKI'S THEOREM 303
11 SELECTED TOPICS 306
11.1 STOCHASTIC DIFFERENTIAL EQUATIONS 306
11.1.1 ITO INTEGRAL 307
11.1.2 DEFINITION O F A MILD SOLUTION 308
11.1.3 EXISTENCE AND UNIQUENESS 311
11.1.4 GLOBAL EXISTENCE AND UNIQUENESS 321
11.2 IMPULSIVE SWEEPING PROCESSES 327
11.2.1 PRELIMINARIES IN NONSMOOTH ANALYSIS 327
11.2.2 UNIQUENESS RESULT 328
11.3 INTEGRAL INCLUSIONS O F VOLTERRA TYPE IN BANACH SPACES 331
11.3.1 RESOLVENT FAMILY 332
11.3.2 EXISTENCE RESULTS 334
11.3.3 THE CONVEX CASE: AN MNC APPROACH 339
11.3.4 THE NONCONVEX CASE 342
11.4 FILIPPOV'S THEOREM 346
11.4.1 FILIPPOV'S THEOREM ON A BOUNDED INTERVAL 346
11.5 THE RELAXED PROBLEM 351
APPENDIX 357
A . L CECH HOMOLOGY FUNCTOR WITH COMPACT CARRIERS 357
A.2 THE BOCHNER INTEGRAL 359
A.3 ABSOLUTELY CONTINUOUS FUNCTIONS 361
A.4 COMPACTNESS CRITERIA IN C([A, B ], E ) , Q,([0, OO), E ) , AND P C (
[ A , B ] , E ) 363
A.5 WEAK-COMPACTNESS IN L 1 365
A.6 PROPER MAPS AND VECTOR FIELDS 367
A.7 FUNDAMENTAL THEOREMS IN FUNCTIONAL ANALYSIS 367
BIBLIOGRAPHY 369
INDEX 399 |
| any_adam_object | 1 |
| author | Graef, John R. 1942- Henderson, Johnny Ouahab, Abdelghani |
| author_GND | (DE-588)140965459 (DE-588)170788350 |
| author_facet | Graef, John R. 1942- Henderson, Johnny Ouahab, Abdelghani |
| author_role | aut aut aut |
| author_sort | Graef, John R. 1942- |
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| building | Verbundindex |
| bvnumber | BV041456588 |
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| 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.BV041456588 |
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| indexdate | 2024-08-03T01:06:49Z |
| institution | BVB |
| isbn | 9783110293616 |
| language | English |
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| physical | X, 400 S. 25 cm |
| publishDate | 2013 |
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| publisher | de Gruyter |
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| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Graef, John R. 1942- Verfasser (DE-588)140965459 aut Impulsive differential inclusions a fixed point approach John R. Graef ; Johnny Henderson ; Abdelghani Ouahab Berlin [u.a.] de Gruyter 2013 X, 400 S. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications 20 Literaturverz. S. [369] - 397 Differentialinklusion (DE-588)4149777-6 gnd rswk-swf Fixpunkt-Methode (DE-588)4139170-6 gnd rswk-swf Impulsdifferentialgleichung (DE-588)4339336-6 gnd rswk-swf Impulsdifferentialgleichung (DE-588)4339336-6 s Differentialinklusion (DE-588)4149777-6 s Fixpunkt-Methode (DE-588)4139170-6 s DE-604 Henderson, Johnny Verfasser (DE-588)170788350 aut Ouahab, Abdelghani Verfasser aut Erscheint auch als Online-Ausgabe 978-3-11-029531-3 De Gruyter series in nonlinear analysis and applications 20 (DE-604)BV005530011 20 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4284927&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026903038&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graef, John R. 1942- Henderson, Johnny Ouahab, Abdelghani Impulsive differential inclusions a fixed point approach De Gruyter series in nonlinear analysis and applications Differentialinklusion (DE-588)4149777-6 gnd Fixpunkt-Methode (DE-588)4139170-6 gnd Impulsdifferentialgleichung (DE-588)4339336-6 gnd |
| subject_GND | (DE-588)4149777-6 (DE-588)4139170-6 (DE-588)4339336-6 |
| title | Impulsive differential inclusions a fixed point approach |
| title_auth | Impulsive differential inclusions a fixed point approach |
| title_exact_search | Impulsive differential inclusions a fixed point approach |
| title_full | Impulsive differential inclusions a fixed point approach John R. Graef ; Johnny Henderson ; Abdelghani Ouahab |
| title_fullStr | Impulsive differential inclusions a fixed point approach John R. Graef ; Johnny Henderson ; Abdelghani Ouahab |
| title_full_unstemmed | Impulsive differential inclusions a fixed point approach John R. Graef ; Johnny Henderson ; Abdelghani Ouahab |
| title_short | Impulsive differential inclusions |
| title_sort | impulsive differential inclusions a fixed point approach |
| title_sub | a fixed point approach |
| topic | Differentialinklusion (DE-588)4149777-6 gnd Fixpunkt-Methode (DE-588)4139170-6 gnd Impulsdifferentialgleichung (DE-588)4339336-6 gnd |
| topic_facet | Differentialinklusion Fixpunkt-Methode Impulsdifferentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4284927&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=026903038&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
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