Generalized topological degree and semilinear equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
117 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 240 S. |
| ISBN: | 0521444748 |
Internformat
MARC
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| 245 | 1 | 0 | |a Generalized topological degree and semilinear equations |c Wolodymyr V. Petryshyn |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface page ix
Introduction 1
1 Introduction to the Brouwer and Leray Schauder
Degrees, A Proper Mappings, and Linear Theory 5
1.1 Definition of the Brouwer Degree for C Functions in
UN and Some Properties 5
1.2 Some Applications 7
1.3 Approximation Schemes, Definitions, and Some
Examples of A Proper Mappings 12
1.4 Further Examples of A Proper Mappings and Some
Constructive Solvability Results 16
1.5 Leray Schauder Degree and Some of Its Properties 22
1.6 Additional Properties, Constructive Solvability,
Fredholm Property of A Proper Linear Maps 24
2 Generalized Degree for Densely Defined A Proper
Mappings, with Some Applications to Semilinear
Equations 29
2.1 Introductory Remarks of an Historical Nature 29
2.2 Definition of the Generalized Degree for Densely
Defined A Proper Mappings 30
2.3 Fixed Point Index for PrCompact Maps 37
2.4 Some Results Using Generalized Degree in Solving
Semilinear Equations 40
2.5 New Approach to the Solvability of Semilinear
Equations 50
vii
viii Contents
2.6 Global Bifurcation Involving A Proper Maps 55
2.7 Parity and Bifurcation Involving C1 Maps 57
3 Solvability of Periodic Semilinear ODEs at
Resonance 65
3.1 Application to Periodic ODEs of Order 2 65
3.2 Special Cases 72
3.3 Application to ODEs of Order n 2 80
3.4 Further Application to Higher Order Equations at
Resonance 96
3.5 Global Bifurcation of Second Order Equations with
Parameter 106
4 Semiconstructive Solvability, Existence Theorems,
and Structure of the Solution Set 111
4.1 Rothe Type Results for Pr Compact Maps 111
4.2 Extension of Results of the Landesman Lazer Type 116
4.3 Fredholm Alternative and Perturbation Results 125
4.4 New A Proper Mapping Results 134
4.5 Improved Solvability Results in Terms of Ym 140
4.6 Structure of the Solution Set and Some Applications 149
5 Solvability of Semilinear PDEs at Resonance 161
5.1 Weak or Variational Solvability of Elliptic Equations 162
5.2 Special Cases 168
5.3 Strong Solvability of Elliptic Equations 175
5.4 Nonresonance and Existence for Semilinear BVPs 184
5.5 Special Problems 192
5.6 Existence of an Unbounded Set of Solutions of
Semilinear PDEs and Its Covering Dimension 202
Appendix 215
References 225
Index 239
|
| any_adam_object | 1 |
| author | Petryshyn, Wolodymyr V. |
| author_facet | Petryshyn, Wolodymyr V. |
| author_role | aut |
| author_sort | Petryshyn, Wolodymyr V. |
| author_variant | w v p wv wvp |
| building | Verbundindex |
| bvnumber | BV010517985 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)243819121 (DE-599)BVBBV010517985 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010517985 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:54:22Z |
| institution | BVB |
| isbn | 0521444748 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007011205 |
| oclc_num | 243819121 |
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| owner | DE-12 DE-703 DE-11 DE-634 DE-188 |
| owner_facet | DE-12 DE-703 DE-11 DE-634 DE-188 |
| physical | X, 240 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Petryshyn, Wolodymyr V. Verfasser aut Generalized topological degree and semilinear equations Wolodymyr V. Petryshyn 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 X, 240 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 117 Abbildungsgrad (DE-588)4140975-9 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Abbildungsgrad (DE-588)4140975-9 s Randwertproblem (DE-588)4048395-2 s DE-604 Cambridge tracts in mathematics 117 (DE-604)BV000000001 117 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007011205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petryshyn, Wolodymyr V. Generalized topological degree and semilinear equations Cambridge tracts in mathematics Abbildungsgrad (DE-588)4140975-9 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4140975-9 (DE-588)4048395-2 |
| title | Generalized topological degree and semilinear equations |
| title_auth | Generalized topological degree and semilinear equations |
| title_exact_search | Generalized topological degree and semilinear equations |
| title_full | Generalized topological degree and semilinear equations Wolodymyr V. Petryshyn |
| title_fullStr | Generalized topological degree and semilinear equations Wolodymyr V. Petryshyn |
| title_full_unstemmed | Generalized topological degree and semilinear equations Wolodymyr V. Petryshyn |
| title_short | Generalized topological degree and semilinear equations |
| title_sort | generalized topological degree and semilinear equations |
| topic | Abbildungsgrad (DE-588)4140975-9 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Abbildungsgrad Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007011205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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