Method of guiding functions in problems of nonlinear analysis:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture notes in mathematics
2076 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 177 S. 235 mm x 155 mm |
| ISBN: | 3642370691 9783642370694 |
Internformat
MARC
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| 245 | 1 | 0 | |a Method of guiding functions in problems of nonlinear analysis |c Valeri Obukhovskii ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIII, 177 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| adam_text |
CONTENTS
1 BACKGROUND 1
1.1 MULTIMAPS 1
1.1.1 GENERAL PROPERTIES 1
1.1.2 MEASURABLE MULTIFUNCTIONS AND SUPERPOSITION
MULTIOPERATOR 5
1.1.3 SINGLE-VALUED APPROXIMATIONS 8
1.2 TOPOLOGICAL DEGREE 12
1.3 COINCIDENCE DEGREE 18
1.4 PHASE SPACES 22
1.5 NOTATION 24
2 METHOD OF GUIDING FUNCTIONS IN FINITE-DIMENSIONAL SPACES 25
2.1 PERIODIC PROBLEM FOR A DIFFERENTIAL INCLUSION 25
2.2 NON-SMOOTH GUIDING FUNCTIONS 36
2.3 INTEGRAL GUIDING FUNCTIONS 39
2.4 GENERALIZED PERIODIC PROBLEMS 43
2.4.1 PRELIMINARIES 43
2.4.2 THE SETTING OF THE PROBLEM 44
2.4.3 APPLICATION TO DIFFERENTIAL GAMES 45
2.4.4 EXISTENCE THEOREM, COROLLARIES AND EXAMPLE 46
2.5 GLOBAL BIFURCATION PROBLEMS 50
2.5.1 ABSTRACT RESULT 51
2.5.2 GLOBAL BIFURCATION OF PERIODIC SOLUTIONS 52
2.5.3 APPLICATION 1: DIFFERENTIAL INCLUSION
WITH A BOUNDED NONLINEARITY 63
2.5.4 APPLICATION 2: GLOBAL BIFURCATION FOR FUNCTIONAL
DIFFERENTIAL INCLUSIONS 64
2.5.5 APPLICATION 3: FEEDBACK CONTROL SYSTEM 65
HTTP://D-NB.INFO/1031344659
VIII CONTENTS
3 METHOD OF GUIDING FUNCTIONS IN HILBERT SPACES 69
3.1 INTEGRAL GUIDING FUNCTIONS FOR DIFFERENTIAL INCLUSIONS
IN HILBERT SPACES 69
3.1.1 THE SETTING OF THE PROBLEM 69
3.1.2 EXISTENCE OF PERIODIC SOLUTIONS 72
3.1.3 APPROXIMATION CONDITIONS 77
3.1.4 APPLICATION 1: CONTROL PROBLEM OF A PARTIAL
DIFFERENTIAL EQUATION 80
3.2 NON-SMOOTH GUIDING FUNCTIONS FOR FUNCTIONAL
DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY IN HILBERT SPACES 83
3.2.1 SETTING OF THE PROBLEM 83
3.2.2 EXISTENCE THEOREM 86
3.2.3 APPLICATION: EXISTENCE OF PERIODIC SOLUTIONS
FOR A GRADIENT FUNCTIONAL DIFFERENTIAL INCLUSION 90
3.3 BIFURCATION PROBLEM 93
3.3.1 THE SETTING OF THE PROBLEM 93
3.3.2 GLOBAL BIFURCATION THEOREM 96
3.3.3 APPLICATION 3: ORDINARY FEEDBACK CONTROL
SYSTEMS IN A HILBERT SPACE 102
4 SECOND-ORDER DIFFERENTIAL INCLUSIONS 105
4.1 EXISTENCE THEOREM IN AN ONE-DIMENSIONAL SPACE 105
4.2 APPLICATIONS 110
4.2.1 EQUATIONS WITH DISCONTINUOUS NONLINEARITIES 110
4.2.2 BOUNDARY VALUE PROBLEM 113
4.2.3 A SECOND-ORDER DIFFERENTIAL EQUATION 114
4.2.4 FEEDBACK CONTROL SYSTEMS 114
4.2.5 A MODEL OF A MOTION OF A PARTICLE IN A
ONE-DIMENSIONAL POTENTIAL 118
4.3 EXISTENCE THEOREM IN HILBERT SPACES 120
4.3.1 APPLICATION TO A SECOND-ORDER FEEDBACK CONTROL
SYSTEM IN HILBERT SPACE 122
4.3.2 EXAMPLE 127
5 NONLINEAR FREDHOLM INCLUSIONS AND APPLICATIONS 131
5.1 PRELIMINARIES 131
5.2 ORIENTED COINCIDENCE INDEX 133
5.2.1 THE CASE OF A FINITE DIMENSIONAL TRIPLET 134
5.2.2 THE CASE OF A COMPACT TRIPLET 138
5.2.3 ORIENTED COINCIDENCE INDEX FOR CONDENSING TRIPLETS 139
5.3 CALCULATION OF THE ORIENTED COINCIDENCE INDEX BY THE MGF 145
5.3.1 THE MAIN RESULT 145
5.3.2 EXAMPLE 153
CONTENTS IX
5.4 GLOBAL BIFURCATION PROBLEM 155
5.4.1 ABSTRACT RESULT 155
5.4.2 GLOBAL BIFURCATION FOR FAMILIES OF PERIODIC TRAJECTORIES 158
5.4.3 EXAMPLE 163
REFERENCES 167
INDEX 175 |
| any_adam_object | 1 |
| author_GND | (DE-588)122814215 |
| building | Verbundindex |
| bvnumber | BV041092721 |
| classification_rvk | SI 850 |
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| ctrlnum | (OCoLC)847104078 (DE-599)DNB1031344659 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-08-03T00:44:05Z |
| institution | BVB |
| isbn | 3642370691 9783642370694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026069286 |
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| physical | XIII, 177 S. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Method of guiding functions in problems of nonlinear analysis Valeri Obukhovskii ... Berlin [u.a.] Springer 2013 XIII, 177 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2076 Differentialinklusion (DE-588)4149777-6 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 s Verzweigung Mathematik (DE-588)4078889-1 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Differentialinklusion (DE-588)4149777-6 s DE-604 Obuchovskij, Valerij 1947- Sonstige (DE-588)122814215 oth Erscheint auch als Online-Ausgabe 978-3-642-37070-0 Lecture notes in mathematics 2076 (DE-604)BV000676446 2076 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4255325&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=026069286&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Method of guiding functions in problems of nonlinear analysis Lecture notes in mathematics Differentialinklusion (DE-588)4149777-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4149777-6 (DE-588)4199269-6 (DE-588)4078889-1 (DE-588)4020929-5 |
| title | Method of guiding functions in problems of nonlinear analysis |
| title_auth | Method of guiding functions in problems of nonlinear analysis |
| title_exact_search | Method of guiding functions in problems of nonlinear analysis |
| title_full | Method of guiding functions in problems of nonlinear analysis Valeri Obukhovskii ... |
| title_fullStr | Method of guiding functions in problems of nonlinear analysis Valeri Obukhovskii ... |
| title_full_unstemmed | Method of guiding functions in problems of nonlinear analysis Valeri Obukhovskii ... |
| title_short | Method of guiding functions in problems of nonlinear analysis |
| title_sort | method of guiding functions in problems of nonlinear analysis |
| topic | Differentialinklusion (DE-588)4149777-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differentialinklusion Periodische Lösung Verzweigung Mathematik Gewöhnliche Differentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4255325&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=026069286&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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