Condensing multivalued maps and semilinear differential inclusions in Banach spaces:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
<<de>> Gruyter
2001
|
| Series: | De Gruyter series in nonlinear analysis and applications
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 213 - 228 |
| Physical Description: | XI, 231 S. 25 cm |
| ISBN: | 3110169894 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013694454 | ||
| 003 | DE-604 | ||
| 005 | 20011030 | ||
| 007 | t | ||
| 008 | 010417s2001 gw |||| |||| 00||| eng d | ||
| 016 | 7 | |a 961228687 |2 DE-101 | |
| 020 | |a 3110169894 |c Pp. : DM 196.00, EUR 98.00, sfr 169.00, S 1431.00 |9 3-11-016989-4 | ||
| 035 | |a (OCoLC)441057215 | ||
| 035 | |a (DE-599)BVBBV013694454 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-824 |a DE-11 |a DE-188 | ||
| 080 | |a 517.9 | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 100 | 1 | |a Kamenskij, Michail |d 1950- |e Verfasser |0 (DE-588)122814185 |4 aut | |
| 245 | 1 | 0 | |a Condensing multivalued maps and semilinear differential inclusions in Banach spaces |c Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca |
| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2001 | |
| 300 | |a XI, 231 S. |b 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v 7 | |
| 500 | |a Literaturverz. S. 213 - 228 | ||
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mengenwertige Abbildung |0 (DE-588)4270772-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialinklusion |0 (DE-588)4149777-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 0 | 1 | |a Mengenwertige Abbildung |0 (DE-588)4270772-9 |D s |
| 689 | 0 | 2 | |a Differentialinklusion |0 (DE-588)4149777-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Obuchovskij, Valerij |d 1947- |e Verfasser |0 (DE-588)122814215 |4 aut | |
| 700 | 1 | |a Zecca, Pietro |d 1949- |e Verfasser |0 (DE-588)122814231 |4 aut | |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v 7 |w (DE-604)BV005530011 |9 7 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009358740 | ||
Record in the Search Index
| _version_ | 1804128509928407040 |
|---|---|
| adam_text | Contents
Introduction v
1 Multivalued maps: general properties 1
1.1 Continuity of multimaps 2
1.2 Operations on multimaps. Selections and approximations 8
1.2.1 Union and intersection of multimaps 8
1.2.2 Composition and Cartesian product of multimaps 14
1.2.3 Algebraic operations on multimaps 17
1.2.4 Selections and approximations 19
1.3 Measurable multimaps and the superposition multioperator 20
1.3.1 Measurable multimaps and multivalued integral 20
1.3.2 The Caratheodory conditions and the Filippov Implicit
Function Lemma 26
1.3.3 The superposition multioperator 28
Bibliographic notes 31
2 Measures of noncompactness and condensing multimaps 33
2.1 Measures of noncompactness 33
2.1.1 Basic notions 33
2.1.2 The expression for the Hausdorff MNC in a separable
Banach space 35
2.1.3 MNC in spaces of continuous functions 36
2.2 Condensing multimaps 41
Bibliographic notes 47
3 Topological degree theory for condensing multifields 49
3.1 The relative topological degree and fixed points of compact multimaps 49
3.2 Topological degree for condensing multifields 55
3.2.1 The definition of the degree 55
3.2.2 The relative topological degree for fundamentally restrictible
multifields defined on the boundary 57
3.2.3 Topological degree for condensing multifields via compact
homotopy approximations 58
3.3 The evaluation of the degree 60
3.3.1 Some fixed point theorems 60
x Contents
3.3.2 Topological degree of equivariant multifields 63
3.4 The topological degree for condensing nonconvex valued multimaps . 67
3.4.1 Vietoris pairs and multimaps 67
3.4.2 The coincidence index for a Vietoris pair in a finite dimensional
space 69
3.4.3 The topological degree for a completely fundamentally
restrictible Vietoris multimap 70
3.4.4 Remark on single valued approximations of nonconvex
valued multimaps 75
3.5 Some properties of the fixed points set 77
3.6 Solvability of systems of inclusions with condensing multioperators . 80
3.6.1 Preliminaries 80
3.6.2 Systems of inclusions 85
3.6.3 Application: optimal control for a neutral functional
differential equation 91
Bibliographic notes 97
4 Semigroups and measures of noncompactness 99
4.1 Semigroups: general facts 99
4.2 Measures of noncompactness in function spaces: measurability and
integrability 106
4.3 Condensing semigroups 117
Bibliographic notes 121
5 Semilinear differential inclusions: initial problem 122
5.1 Integral multioperator 122
5.2 Existence and continuous dependence theorems 129
5.2.1 Local and global existence results. Regularity properties
of solutions. Some examples 129
5.2.2 Optimization of semilinear feedback control systems 139
5.2.3 On the index of the solutions set 142
5.2.4 Continuous dependence of the solutions set on parameters and
initial data 143
5.3 The structure of the solutions set 147
5.4 The averaging principle 153
5.5 On inclusions with almost lower semicontinuous nonlinearities .... 161
Bibliographic notes 172
6 Semilinear inclusions: periodic problems 175
6.1 The integral multioperator for a periodic problem 175
6.2 The averaging principle for a periodic problem 187
6.3 The translation multioperator 197
Contents xi
6.3.1 The translation multioperator along the solutions of semilinear
differential inclusions 197
6.3.2 Dissipative differential inclusions: periodic solutions and
attractors 207
Bibliographic notes 211
Bibliography 213
Index 229
|
| any_adam_object | 1 |
| author | Kamenskij, Michail 1950- Obuchovskij, Valerij 1947- Zecca, Pietro 1949- |
| author_GND | (DE-588)122814185 (DE-588)122814215 (DE-588)122814231 |
| author_facet | Kamenskij, Michail 1950- Obuchovskij, Valerij 1947- Zecca, Pietro 1949- |
| author_role | aut aut aut |
| author_sort | Kamenskij, Michail 1950- |
| author_variant | m k mk v o vo p z pz |
| building | Verbundindex |
| bvnumber | BV013694454 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)441057215 (DE-599)BVBBV013694454 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02033nam a2200457 cb4500</leader><controlfield tag="001">BV013694454</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20011030 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010417s2001 gw |||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">961228687</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110169894</subfield><subfield code="c">Pp. : DM 196.00, EUR 98.00, sfr 169.00, S 1431.00</subfield><subfield code="9">3-11-016989-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)441057215</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013694454</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="080" ind1=" " ind2=" "><subfield code="a">517.9</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kamenskij, Michail</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122814185</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Condensing multivalued maps and semilinear differential inclusions in Banach spaces</subfield><subfield code="c">Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; New York</subfield><subfield code="b"><<de>> Gruyter</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 231 S.</subfield><subfield code="b">25 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">7</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 213 - 228</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mengenwertige Abbildung</subfield><subfield code="0">(DE-588)4270772-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialinklusion</subfield><subfield code="0">(DE-588)4149777-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mengenwertige Abbildung</subfield><subfield code="0">(DE-588)4270772-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Differentialinklusion</subfield><subfield code="0">(DE-588)4149777-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Obuchovskij, Valerij</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122814215</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zecca, Pietro</subfield><subfield code="d">1949-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122814231</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">7</subfield><subfield code="w">(DE-604)BV005530011</subfield><subfield code="9">7</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009358740</subfield></datafield></record></collection> |
| id | DE-604.BV013694454 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:50:23Z |
| institution | BVB |
| isbn | 3110169894 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009358740 |
| oclc_num | 441057215 |
| open_access_boolean | |
| owner | DE-824 DE-11 DE-188 |
| owner_facet | DE-824 DE-11 DE-188 |
| physical | XI, 231 S. 25 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Kamenskij, Michail 1950- Verfasser (DE-588)122814185 aut Condensing multivalued maps and semilinear differential inclusions in Banach spaces Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca Berlin ; New York <<de>> Gruyter 2001 XI, 231 S. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications 7 Literaturverz. S. 213 - 228 Banach-Raum (DE-588)4004402-6 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 gnd rswk-swf Differentialinklusion (DE-588)4149777-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Mengenwertige Abbildung (DE-588)4270772-9 s Differentialinklusion (DE-588)4149777-6 s DE-604 Obuchovskij, Valerij 1947- Verfasser (DE-588)122814215 aut Zecca, Pietro 1949- Verfasser (DE-588)122814231 aut De Gruyter series in nonlinear analysis and applications 7 (DE-604)BV005530011 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kamenskij, Michail 1950- Obuchovskij, Valerij 1947- Zecca, Pietro 1949- Condensing multivalued maps and semilinear differential inclusions in Banach spaces De Gruyter series in nonlinear analysis and applications Banach-Raum (DE-588)4004402-6 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Differentialinklusion (DE-588)4149777-6 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4270772-9 (DE-588)4149777-6 |
| title | Condensing multivalued maps and semilinear differential inclusions in Banach spaces |
| title_auth | Condensing multivalued maps and semilinear differential inclusions in Banach spaces |
| title_exact_search | Condensing multivalued maps and semilinear differential inclusions in Banach spaces |
| title_full | Condensing multivalued maps and semilinear differential inclusions in Banach spaces Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca |
| title_fullStr | Condensing multivalued maps and semilinear differential inclusions in Banach spaces Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca |
| title_full_unstemmed | Condensing multivalued maps and semilinear differential inclusions in Banach spaces Mikhail Kamenskii ; Valeri Obukhovskii ; Pietro Zecca |
| title_short | Condensing multivalued maps and semilinear differential inclusions in Banach spaces |
| title_sort | condensing multivalued maps and semilinear differential inclusions in banach spaces |
| topic | Banach-Raum (DE-588)4004402-6 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Differentialinklusion (DE-588)4149777-6 gnd |
| topic_facet | Banach-Raum Mengenwertige Abbildung Differentialinklusion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT kamenskijmichail condensingmultivaluedmapsandsemilineardifferentialinclusionsinbanachspaces AT obuchovskijvalerij condensingmultivaluedmapsandsemilineardifferentialinclusionsinbanachspaces AT zeccapietro condensingmultivaluedmapsandsemilineardifferentialinclusionsinbanachspaces |