Nonlinear differential equations in abstract spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1981
|
| Schriftenreihe: | International series in nonlinear mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 258 S. |
| ISBN: | 0080250386 |
Internformat
MARC
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| 100 | 1 | |a Lakshmikantham, Vangipuram |d 1926- |e Verfasser |0 (DE-588)104268050 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear differential equations in abstract spaces |c by V. Lakshmikantham and S. Leela |
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1981 | |
| 300 | |a X, 258 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series in nonlinear mathematics |v 2 | |
| 490 | 0 | |a Pergamon international library of science, technology, engineering and social studies | |
| 650 | 7 | |a Banachruimten |2 gtt | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Niet-lineaire vergelijkingen |2 gtt | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |D s |
| 689 | 0 | 1 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
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| 689 | 1 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 1 | 1 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Leela, Srinivasa |d 1936- |e Verfasser |0 (DE-588)123072417 |4 aut | |
| 830 | 0 | |a International series in nonlinear mathematics |v 2 |w (DE-604)BV002809947 |9 2 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001489312 | ||
Datensatz im Suchindex
| _version_ | 1804116724138639360 |
|---|---|
| adam_text | Contents
CHAPTER 1
1.0 Introduction 1
1.1 Preliminaries 1
1.2 Directional Derivatives 7
1.3 Mean Value Theorems 13
1.4 Measures of Noncompactness 17
1.5 Measure of Weak Noncompactness 24
1.6 Comparison Results 26
1.7 Notes and Comments 31
CHAPTER 2
2.0 Introduction 32
2.1 The Cauchy Problem 33
2.2 Successive Approximations 34
2.3 Types of Approximate Solutions 37
2.4 Dissipative Type Conditions 40
2.5 Compactness Type Condtions 44
2.6 Existence in Closed Sets 50
2.7 Existence in Closed Sets (Continued) 58
2.8 Nonlinear Semigroups 66
2.9 Invarlance Criteria 70
2.10 Notes and Comments 75
CHAPTER 3
3.0 Introduction 77
3.1 Dissipative Operators 79
3.2 The Exponential Formula 83
3.3 Difference Approximations 91
3.4 Convergence of Difference Approximations 96
3.5 Integral Solutions 104
3.6 Existence of Limit Solutions 108
3.7 m Dissipative Operators 118
3.8 Perturbation of Dissipative Operators 122
3.9 Invariance of Nonlinear Semigroups 125
3.10 Examples 132
3.11 Compactness Type Condition 137
3.12 Notes and Comments 142
ix
x Contents
CHAPTER 4
4.0 Introduction 144
4.1 Global Existence 144
4.2 Fundamental Properties 149
4.3 Differential Inequalities in Cones 156
4.4 Flow Invariant Sets 161
4.5 Method of Quasilinearization 165
4.6 Asymptotic Equilibrium 169
4.7 Stability and Asymptotic Behavior 175
4.8 Perturbing Lyapunov Functions 179
4.9 Vector Lyapunov Functions 183
4.10 Notes and Comments 185
CHAPTER 5
5.0 Introduction 187
5.1 Existence of Solutions in Weak Topology 187
5.2 Equations with Delay 194
5.3 Boundary Value Problems 210
5.4 Monotone Iterative Methods 217
5.5 Integral Equations 229
5.6 Notes and Comments 243
REFERENCES 244
SUBJECT INDEX 257
|
| any_adam_object | 1 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/55 |
| dewey-search | 515.3/55 |
| dewey-sort | 3515.3 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002266411 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:03Z |
| institution | BVB |
| isbn | 0080250386 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001489312 |
| oclc_num | 7580991 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | X, 258 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series in nonlinear mathematics |
| series2 | International series in nonlinear mathematics Pergamon international library of science, technology, engineering and social studies |
| spelling | Lakshmikantham, Vangipuram 1926- Verfasser (DE-588)104268050 aut Nonlinear differential equations in abstract spaces by V. Lakshmikantham and S. Leela Oxford [u.a.] Pergamon Press 1981 X, 258 S. txt rdacontent n rdamedia nc rdacarrier International series in nonlinear mathematics 2 Pergamon international library of science, technology, engineering and social studies Banachruimten gtt Differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Banach spaces Differential equations, Nonlinear Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Banach-Raum (DE-588)4004402-6 s DE-604 Differentialgleichung (DE-588)4012249-9 s Leela, Srinivasa 1936- Verfasser (DE-588)123072417 aut International series in nonlinear mathematics 2 (DE-604)BV002809947 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926- Leela, Srinivasa 1936- Nonlinear differential equations in abstract spaces International series in nonlinear mathematics Banachruimten gtt Differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Banach spaces Differential equations, Nonlinear Differentialgleichung (DE-588)4012249-9 gnd Banach-Raum (DE-588)4004402-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4004402-6 (DE-588)4205536-2 |
| title | Nonlinear differential equations in abstract spaces |
| title_auth | Nonlinear differential equations in abstract spaces |
| title_exact_search | Nonlinear differential equations in abstract spaces |
| title_full | Nonlinear differential equations in abstract spaces by V. Lakshmikantham and S. Leela |
| title_fullStr | Nonlinear differential equations in abstract spaces by V. Lakshmikantham and S. Leela |
| title_full_unstemmed | Nonlinear differential equations in abstract spaces by V. Lakshmikantham and S. Leela |
| title_short | Nonlinear differential equations in abstract spaces |
| title_sort | nonlinear differential equations in abstract spaces |
| topic | Banachruimten gtt Differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Banach spaces Differential equations, Nonlinear Differentialgleichung (DE-588)4012249-9 gnd Banach-Raum (DE-588)4004402-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Banachruimten Differentiaalvergelijkingen Niet-lineaire vergelijkingen Banach spaces Differential equations, Nonlinear Differentialgleichung Banach-Raum Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002809947 |
| work_keys_str_mv | AT lakshmikanthamvangipuram nonlineardifferentialequationsinabstractspaces AT leelasrinivasa nonlineardifferentialequationsinabstractspaces |