Theorems of Leray-Schauder type and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Gordon and Breach Science publ.
2001
|
| Series: | Series in mathematical analysis and applications
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 206 S. |
| ISBN: | 9056992953 |
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Record in the Search Index
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| adam_text | Titel: Theorems of Leray-Schauder type and applications
Autor: O Regan, Donal
Jahr: 2001
Contents
Preface ix
1. Overview 1
2. Theorems of Leray-Schauder Type for Contractions 9
2.1 The Continuation Principle for Contractions on Spaces with Two Metrics 9
2.2 Global Solutions to the Cauchy Problem on a Bounded Set in
Banach Spaces 18
2.3 Boundary Value Problems on a Bounded Set in Banach Spaces 25
3. Continuation Theorems for Nonexpansive Maps 43
3.1 Continuation Theorems 43
3.2 Elements of Geometry of Sobolev Spaces 47
3.3 Sturm-Liouville Problems in Uniformly Convex Banach Spaces 50
4. Theorems of Leray-Schauder Type for Accretive Maps 53
4.1 Properties of Accretive Maps 53
4.2 Continuation Principles for Accretive Maps 55
4.3 Applications to Boundary Value Problems in Hilbert Spaces 61
5. Continuation Theorems Involving Compactness 65
5.1 Monch Continuation Principle 65
5.2 Granas Topological Transversality Theorem 68
5.3 Measures of Noncompactness on C(I;E) 70
5.4 The Cauchy Problem in Banach Spaces 74
5.5 Sturm-Liouville Problems in Banach Spaces 79
vii
viii CONTENTS
6. Applications to Semilinear Elliptic Problems 83
6.1 Basic Results from the Theory of Linear Elliptic Equations 84
6.2 Applications oftheBanach,Schauder and Darbo Fixed Point Theorems 88
6.3 Applications of the Leray-Schauder Type Theorems 91
7. Theorems of Leray-Schauder Type for Coincidences 101
7.1 Continuation Principles for Coincidences 101
7.2 Application to Periodic Solutions of Differential Systems 107
8. Theorems of Selective Continuation 111
8.1 Selective Continuation Principles 111
8.2 Con tinua of Solutions 115
8.3 Continuation with Respect to a Functional 118
8.4 Periodic Solutions ofSuperlinear Singular Boundary Value Problems 120
9. The Unified Theory 137
9.1 A General Continuation Principle 137
9.2 A General Fixed Point Continuation Principle 143
9.3 Continuation Theorems for Maps of Monotone Type 147
10. Multiplicity 155
10.1 Leray-Schauder Theorems of Compression-Expansion Type 155
10.2 Multiple Solutions of Focal Boundary Value Problems 163
11. Local Continuation Theorems 171
11.1 Local Continuation Theorems for Contractions 172
11.2 The Classical Implicit Function Theorem 176
11.3 Two Special Local Continuation Theorems 179
11.4 Continuation and Stability 181
Epilogue 189
Bibliography jgj
Index
205
|
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| indexdate | 2024-07-09T19:04:58Z |
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| isbn | 9056992953 |
| language | English |
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| physical | VIII, 206 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Gordon and Breach Science publ. |
| record_format | marc |
| series | Series in mathematical analysis and applications |
| series2 | Series in mathematical analysis and applications |
| spelling | O'Regan, Donal Verfasser aut Theorems of Leray-Schauder type and applications Donal O'Regan and Radu Precup New York [u.a.] Gordon and Breach Science publ. 2001 VIII, 206 S. txt rdacontent n rdamedia nc rdacarrier Series in mathematical analysis and applications 3 Schauderscher Fixpunktsatz (DE-588)4179417-5 gnd rswk-swf Nichtlinearer Operator (DE-588)4225824-8 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Schauderscher Fixpunktsatz (DE-588)4179417-5 s Nichtlinearer Operator (DE-588)4225824-8 s Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Precup, Radu 1955- Verfasser (DE-588)1028201435 aut Series in mathematical analysis and applications 3 (DE-604)BV013405523 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009956967&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Regan, Donal Precup, Radu 1955- Theorems of Leray-Schauder type and applications Series in mathematical analysis and applications Schauderscher Fixpunktsatz (DE-588)4179417-5 gnd Nichtlinearer Operator (DE-588)4225824-8 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd |
| subject_GND | (DE-588)4179417-5 (DE-588)4225824-8 (DE-588)4177490-5 |
| title | Theorems of Leray-Schauder type and applications |
| title_auth | Theorems of Leray-Schauder type and applications |
| title_exact_search | Theorems of Leray-Schauder type and applications |
| title_full | Theorems of Leray-Schauder type and applications Donal O'Regan and Radu Precup |
| title_fullStr | Theorems of Leray-Schauder type and applications Donal O'Regan and Radu Precup |
| title_full_unstemmed | Theorems of Leray-Schauder type and applications Donal O'Regan and Radu Precup |
| title_short | Theorems of Leray-Schauder type and applications |
| title_sort | theorems of leray schauder type and applications |
| topic | Schauderscher Fixpunktsatz (DE-588)4179417-5 gnd Nichtlinearer Operator (DE-588)4225824-8 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd |
| topic_facet | Schauderscher Fixpunktsatz Nichtlinearer Operator Nichtlineare Analysis |
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