Nonlinear semigroups and differential equations in Banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bucureşti [u.a.]
Ed. Acad. [u.a.]
1976
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 352 S. |
| ISBN: | 9028602054 9789028602052 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear semigroups and differential equations in Banach spaces |c Viorel Barbu |
| 264 | 1 | |a Bucureşti [u.a.] |b Ed. Acad. [u.a.] |c 1976 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the first edition 9
Preface to the English edition 10
Chapter I
PRELIMINARIES
§ 1. Metric properties of normed spaces II
1.1 Duality mappings 11
1.2 Strictly convex normed spaces 13
1.3 Uniformly convex Banach spaces 14
§ 2. Vectorial functions defined on real intervals 15
2.1 Absolutely continuous vectorial functions 15
2.2 Vectorial distributions and Wk p spaces 18
2.3 Sobolev spaces 21
§ 3. Semigroups of continuous linear operators 24
3.1 Semigroups of class (Co). Hille Yosida theorem 24
3.2 Analytic semigroups 29
3.3 Nonhomogeneous linear differential equations 30
Chapter II
NONLINEAR OPERATORS IN BANACH SPACES
§ 1. Maximal monotone operators 33
1.1 Definitions and fundamental concepts 33
1.2 A general perturbation theorem 41
1.3 A nonlinear elliptic boundary problem 48
5
Contents
§ 2. Subdifferential mappings 50
2.1 Lower semicontinuous convex functions 50
2.2 Subdifferentials of convex functions 52
2.3 Some examples of cyclically monotone operators 60
§ 3. Dissipative sets in Banach spaces 71
3.1 Basic properties of dissipative sets 71
3.2 Perturbations of dissipative sets 80
3.3 Riccati equations in Hilbert spaces 89
Bibliographical notes 96
Chapter III
DIFFERENTIAL EQUATIONS IN BANACH SPACES
§ 1. Semigroups of nonlinear contractions in Banach spaces 98
1.1 General properties of nonlinear semigroups 98
1.2 The exponential formula 104
1.3 Convergence theorems 108
1.4 Generation of nonlinear semigroups 115
§ 2. Quasi autonomous differential equations 123
2.1 Existence theorems 123
2.2 Periodic solutions 138
2.3 Examples 139
§ 3. Differential equations associated with continuous dissipative operators 152
3.1 A general existence result 152
3.2 Continuous perturbations of /n dissipative operators 158
3.3 Semi linear second order elliptic equations in L1 160 !
§ 4. Time dependent nonlinear differential equations 164
4.1 Evolution equations associated with dissipative sets 164
4.2 Evolution equations associated with nonlinear monotone hemicon
tinuous operators 166
Bibliographical notes 168
6
Contents
Chapter IV
NONLINEAR DIFFERENTIAL EQUATIONS IN HILBERT SPACES
§ 1. Nonlinear semigroups in Hilbert spaces 171
1.1 Nonlinear version of the Hille Yosida theorem 171
1.2 Exponential formulae 177
1.3 Invariant sets with respect to nonlinear semigroups 182
§ 2. Smoothing effect on initial data 188
2.1 The case in which A = dtp 188
2.2 The case in which int D{A) # 0 197
2.3 Applications 200
§ 3. Variational evolution inequations 207
3.1 Unilateral conditions on u{t) 208
3.2 Unilateral conditions on —(/) 212
df
3.3 A class of nonlinear variational inequations 218
3.4 Applications 226
§ 4. Nonlinear Volterra equations with positive kernels in Hilbert spaces 235
4.1 Positive kernels 236
4.2 Equation (4.1) with A = d p 239
4.3 Equation (4.1) with A demicontinuous 248
4.4 A class of integro differential equations 252
4.5 Further investigation of the preceding case 261
Bibliographical notes 265
Chapter V
SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS
§ 1. Nonlinear differential equations of hyperbolic type 267
1.1 The equation — + Au + Aff^W 267
d/2 dt )
1.2 Further investigation of the preceding case 270
7
Contents
1.3 Examples 279
1.4 Singular perturbations and hyperbolic variational inequations 283
1.5 Nonlinear wave equation 288
§ 2. Boundary value problems for second order nonlinear differential
equations 300
2.1 A class of two point boundary value problems 300
2.2 Examples 309
2.3 A boundary value problem on half axis 315
2.4 The square root of a nonlinear maximal monotone operator 329
Bibliographical notes 339
Bibliography 341
Subject index 351
|
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| bvnumber | BV001966186 |
| classification_rvk | SK 500 SK 620 |
| ctrlnum | (OCoLC)252462195 (DE-599)BVBBV001966186 |
| discipline | Mathematik |
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| id | DE-604.BV001966186 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:03Z |
| institution | BVB |
| isbn | 9028602054 9789028602052 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001282272 |
| oclc_num | 252462195 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-188 DE-83 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-188 DE-83 |
| physical | 352 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Ed. Acad. [u.a.] |
| record_format | marc |
| spelling | Barbu, Viorel 1941- Verfasser (DE-588)1127566091 aut Semigrupuri de contraçtii neliniare în spaţii Banach Nonlinear semigroups and differential equations in Banach spaces Viorel Barbu Bucureşti [u.a.] Ed. Acad. [u.a.] 1976 352 S. txt rdacontent n rdamedia nc rdacarrier Halbgruppe (DE-588)4022990-7 gnd rswk-swf Nichtlineare Halbgruppe (DE-588)4139678-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Halbgruppe (DE-588)4022990-7 s Banach-Raum (DE-588)4004402-6 s DE-604 Nichtlineare Halbgruppe (DE-588)4139678-9 s Erscheint auch als Online-Ausgabe 978-94-010-1537-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barbu, Viorel 1941- Nonlinear semigroups and differential equations in Banach spaces Halbgruppe (DE-588)4022990-7 gnd Nichtlineare Halbgruppe (DE-588)4139678-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4022990-7 (DE-588)4139678-9 (DE-588)4012249-9 (DE-588)4004402-6 |
| title | Nonlinear semigroups and differential equations in Banach spaces |
| title_alt | Semigrupuri de contraçtii neliniare în spaţii Banach |
| title_auth | Nonlinear semigroups and differential equations in Banach spaces |
| title_exact_search | Nonlinear semigroups and differential equations in Banach spaces |
| title_full | Nonlinear semigroups and differential equations in Banach spaces Viorel Barbu |
| title_fullStr | Nonlinear semigroups and differential equations in Banach spaces Viorel Barbu |
| title_full_unstemmed | Nonlinear semigroups and differential equations in Banach spaces Viorel Barbu |
| title_short | Nonlinear semigroups and differential equations in Banach spaces |
| title_sort | nonlinear semigroups and differential equations in banach spaces |
| topic | Halbgruppe (DE-588)4022990-7 gnd Nichtlineare Halbgruppe (DE-588)4139678-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Halbgruppe Nichtlineare Halbgruppe Differentialgleichung Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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