Topological degree theory and applications:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Series: | Series in mathematical analysis and applications
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 221 S. |
| ISBN: | 158488648X 9781584886488 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 BROUWER DEGREE THEORY 1
1.1 Continuous and Differentiable Functions 2
1.2 Construction of Brouwer Degree 4
1.3 Degree Theory for Functions in VMO 15
1.4 Applications to ODEs 19
1.5 Exercises 22
2 LERAY SCHAUDER DEGREE THEORY 25
2.1 Compact Mappings 25
2.2 Leray Schauder Degree 30
2.3 Leray Schauder Degree for Multi Valued Mappings 38
2.4 Applications to Bifurcations 43
2.5 Applications to ODEs and PDEs 46
2.6 Exercises 53
3 DEGREE THEORY FOR SET CONTRACTIVE MAPS 55
3.1 Measure of Noncompactness and Set Contractions 55
3.2 Degree Theory for Countably Condensing Mappings 65
3.3 Applications to ODEs in Banach Spaces 68
3.4 Exercises 71
4 GENERALIZED DEGREE THEORY FOR A PROPER MAPS
75
4.1 A Proper Mappings 75
4.2 Generalized Degree for A Proper Mappings 80
4.3 Equations with Fredholm Mappings of Index Zero 82
4.4 Equations with Fredholm Mappings of Index Zero Type ... 87
4.5 Applications of the Generalized Degree 95
4.6 Exercises 101
5 COINCIDENCE DEGREE THEORY 105
5.1 Fredholm Mappings 105
5.2 Coincidence Degree for L Compact Mappings 110
5.3 Existence Theorems for Operator Equations 116
5.4 Applications to ODEs 119
5.5 Exercises 124
6 DEGREE THEORY FOR MONOTONE TYPE MAPS 127
6.1 Monotone Type Mappings in Reflexive Banach Spaces .... 128
6.2 Degree Theory for Mappings of Class (S+) 142
6.3 Degree for Perturbations of Monotone Type Mappings .... 145
6.4 Degree Theory for Mappings of Class (S+)i 149
6.5 Coincidence Degree for Mappings of Class L (5+) 152
6.6 Computation of Topological Degree 156
6.7 Applications to PDEs and Evolution Equations 159
6.8 Exercises 167
7 FIXED POINT INDEX THEORY 169
7.1 Cone in Normed Spaces 169
7.2 Fixed Point Index Theory 176
7.3 Fixed Point Theorems in Cones 179
7.4 Perturbations of Condensing Mappings 186
7.5 Index Theory for Nonself Mappings 189
7.6 Applications to Integral and Differential Equations 191
7.7 Exercises 193
8 REFERENCES 195
9 SUBJECT INDEX 217
|
| adam_txt |
Contents
1 BROUWER DEGREE THEORY 1
1.1 Continuous and Differentiable Functions 2
1.2 Construction of Brouwer Degree 4
1.3 Degree Theory for Functions in VMO 15
1.4 Applications to ODEs 19
1.5 Exercises 22
2 LERAY SCHAUDER DEGREE THEORY 25
2.1 Compact Mappings 25
2.2 Leray Schauder Degree 30
2.3 Leray Schauder Degree for Multi Valued Mappings 38
2.4 Applications to Bifurcations 43
2.5 Applications to ODEs and PDEs 46
2.6 Exercises 53
3 DEGREE THEORY FOR SET CONTRACTIVE MAPS 55
3.1 Measure of Noncompactness and Set Contractions 55
3.2 Degree Theory for Countably Condensing Mappings 65
3.3 Applications to ODEs in Banach Spaces 68
3.4 Exercises 71
4 GENERALIZED DEGREE THEORY FOR A PROPER MAPS
75
4.1 A Proper Mappings 75
4.2 Generalized Degree for A Proper Mappings 80
4.3 Equations with Fredholm Mappings of Index Zero 82
4.4 Equations with Fredholm Mappings of Index Zero Type . 87
4.5 Applications of the Generalized Degree 95
4.6 Exercises 101
5 COINCIDENCE DEGREE THEORY 105
5.1 Fredholm Mappings 105
5.2 Coincidence Degree for L Compact Mappings 110
5.3 Existence Theorems for Operator Equations 116
5.4 Applications to ODEs 119
5.5 Exercises 124
6 DEGREE THEORY FOR MONOTONE TYPE MAPS 127
6.1 Monotone Type Mappings in Reflexive Banach Spaces . 128
6.2 Degree Theory for Mappings of Class (S+) 142
6.3 Degree for Perturbations of Monotone Type Mappings . 145
6.4 Degree Theory for Mappings of Class (S+)i 149
6.5 Coincidence Degree for Mappings of Class L (5+) 152
6.6 Computation of Topological Degree 156
6.7 Applications to PDEs and Evolution Equations 159
6.8 Exercises 167
7 FIXED POINT INDEX THEORY 169
7.1 Cone in Normed Spaces 169
7.2 Fixed Point Index Theory 176
7.3 Fixed Point Theorems in Cones 179
7.4 Perturbations of Condensing Mappings 186
7.5 Index Theory for Nonself Mappings 189
7.6 Applications to Integral and Differential Equations 191
7.7 Exercises 193
8 REFERENCES 195
9 SUBJECT INDEX 217 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:31:28Z |
| indexdate | 2024-07-09T20:38:25Z |
| institution | BVB |
| isbn | 158488648X 9781584886488 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014766761 |
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| physical | 221 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Series in mathematical analysis and applications |
| series2 | Series in mathematical analysis and applications |
| spelling | O'Regan, Donal Verfasser aut Topological degree theory and applications Donal O'Regan ; Yeol Je Cho ; Yu-Quing Chen Boca Raton [u.a.] Chapman & Hall/CRC 2006 221 S. txt rdacontent n rdamedia nc rdacarrier Series in mathematical analysis and applications 10 Differentiable functions Topological degree Abbildungsgrad (DE-588)4140975-9 gnd rswk-swf Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Abbildungsgrad (DE-588)4140975-9 s DE-604 Fixpunkttheorie (DE-588)4293945-8 s Cho, Yeol Je Verfasser aut Chen, Yu-Qing Verfasser aut Series in mathematical analysis and applications 10 (DE-604)BV013405523 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014766761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Regan, Donal Cho, Yeol Je Chen, Yu-Qing Topological degree theory and applications Series in mathematical analysis and applications Differentiable functions Topological degree Abbildungsgrad (DE-588)4140975-9 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| subject_GND | (DE-588)4140975-9 (DE-588)4293945-8 |
| title | Topological degree theory and applications |
| title_auth | Topological degree theory and applications |
| title_exact_search | Topological degree theory and applications |
| title_exact_search_txtP | Topological degree theory and applications |
| title_full | Topological degree theory and applications Donal O'Regan ; Yeol Je Cho ; Yu-Quing Chen |
| title_fullStr | Topological degree theory and applications Donal O'Regan ; Yeol Je Cho ; Yu-Quing Chen |
| title_full_unstemmed | Topological degree theory and applications Donal O'Regan ; Yeol Je Cho ; Yu-Quing Chen |
| title_short | Topological degree theory and applications |
| title_sort | topological degree theory and applications |
| topic | Differentiable functions Topological degree Abbildungsgrad (DE-588)4140975-9 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| topic_facet | Differentiable functions Topological degree Abbildungsgrad Fixpunkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014766761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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