Theory of Causal Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Amsterdam
Atlantis Press
World Scientific |
| Schriftenreihe: | Atlantis studies in mathematics for engineering and science
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 208 S. |
| ISBN: | 9789078677321 |
Internformat
MARC
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| 245 | 1 | 0 | |a Theory of Causal Differential Equations |c V. Lakshmikantham ... |
| 264 | 1 | |a Amsterdam |b Atlantis Press | |
| 264 | 1 | |a World Scientific | |
| 300 | |a XI, 208 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Atlantis studies in mathematics for engineering and science |v 5 | |
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| 830 | 0 | |a Atlantis studies in mathematics for engineering and science |v 5 |w (DE-604)BV036703056 |9 5 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020621534 | ||
Datensatz im Suchindex
| _version_ | 1804143343940141056 |
|---|---|
| adam_text | Contents
Preface
v
1.
Preliminaries
1
1.1
Introduction
................................. 1
1.2
Causal Operators
.............................. 1
1.3
Known Basic Results
............................ 6
1.4
Fixed Point Theorems and Auxiliary Results
................ 9
1.5
Preliminaries in a Banach Space
...................... 12
1.6
Directional Derivatives
........................... 15
1.7
Measure of Noncompactness
........................ 17
1.8
The Measure of Nonconvexity
....................... 18
1.9
Notes and Comments
............................ 22
2.
Basic Theory
23
2.1
Introduction
................................. 23
2.2
Causal Functional and Differential Inequalities
.............. 24
2.3
Existence and Extremal Solutions
..................... 27
2.4
Global Existence
.............................. 32
2.5
Existence and Uniqueness
......................... 35
2.6
Nagumo-Type Conditions
.......................... 40
2.7
Continuous Dependence Relative to Initial Data
.............. 43
2.8
Existence of
Euler
Solutions
........................ 47
2.9
Flow
Invariance
............................... 51
2.10
Systems of Causal Differential Inequalities
................ 53
IX
x
Theory of Causal Differential Equations
2.11
Nonlinear Variation of Parameters
.....................55
2.12
Integral Equations of Sobolev Type
....................59
2.13
Differential Equations of Sobolev Type
..................65
2.14
Notes and Comments
............................70
3.
Theoretical Approximation Methods
73
3.1
Introduction
.................................73
3.2
Method of Lower and Upper Solutions
...................74
3.3
Monotone Iterative Technique
.......................75
3.4
Generalized Monotone Iterative Technique
.................79
3.5
Monotone Technique for PBVPs
...................... 87
3.6
The Method of Quasilinearization (MQL)
.................91
3.7
Extension of Quasilinearization
......................94
3.8
Newton s Method Versus Quasilinearization
................99
3.9
Notes and Comments
............................102
4.
Stability Theory
105
4.1
Introduction
.................................105
4.2
Comparison Theorems via Lyapunov Functions
..............106
4.3
Definitions of Stability and Boundedness
.................
Ill
4.4
Definitions Relative to Two Measures
...................114
4.5
Stability Criteria-Lyapunov Functions
...................116
4.6
Stability Criteria-Lyapunov Functionals
..................118
4.7
Lyapunov Functions on Product Spaces
..................120
4.8
Stability in Terms of two Measures
.....................123
4.9
Vector Lyapunov Functions
.........................125
4.10
Cone-valued Lyapunov Functions
.....................128
4.11
Notes and Comments
............................136
5.
Miscellaneous Topics in Causal Systems
137
5.1
Introduction
.................................137
5.2
Causal Set Differential Equations
......................138
5.3
Comparison Results and Stability Theory
.................146
5.4
Causal Differential Equations in a Banach Space
.............157
5.5
Global Existence and Inequalities in Cones
................163
Contents
5.6
Fractional Causal Differential Equations
..................169
5.7
Causal Differential Equations with Memory
................175
5.8
Causal Differential Systems with Retardation and Anticipation
......181
5.9
Monotone Iterative Technique
.......................188
5.10
Neutral Differential Equations with Causal Operators on a Semi-Axis
. .193
5.11
Notes and Comments
............................201
Bibliography
203
Subject Index
207
|
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| author | Lakshmikantham, Vangipuram 1926- |
| author_GND | (DE-588)104268050 |
| author_facet | Lakshmikantham, Vangipuram 1926- |
| author_role | aut |
| author_sort | Lakshmikantham, Vangipuram 1926- |
| author_variant | v l vl |
| building | Verbundindex |
| bvnumber | BV036703149 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)699796124 (DE-599)BVBBV036703149 |
| discipline | Mathematik |
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| id | DE-604.BV036703149 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:46:10Z |
| institution | BVB |
| isbn | 9789078677321 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020621534 |
| oclc_num | 699796124 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | XI, 208 S. |
| publishDateSort | 0000 |
| publisher | Atlantis Press |
| record_format | marc |
| series | Atlantis studies in mathematics for engineering and science |
| series2 | Atlantis studies in mathematics for engineering and science |
| spelling | Lakshmikantham, Vangipuram 1926- Verfasser (DE-588)104268050 aut Theory of Causal Differential Equations V. Lakshmikantham ... Amsterdam Atlantis Press World Scientific XI, 208 S. txt rdacontent n rdamedia nc rdacarrier Atlantis studies in mathematics for engineering and science 5 Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 Atlantis studies in mathematics for engineering and science 5 (DE-604)BV036703056 5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020621534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926- Theory of Causal Differential Equations Atlantis studies in mathematics for engineering and science Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Theory of Causal Differential Equations |
| title_auth | Theory of Causal Differential Equations |
| title_exact_search | Theory of Causal Differential Equations |
| title_full | Theory of Causal Differential Equations V. Lakshmikantham ... |
| title_fullStr | Theory of Causal Differential Equations V. Lakshmikantham ... |
| title_full_unstemmed | Theory of Causal Differential Equations V. Lakshmikantham ... |
| title_short | Theory of Causal Differential Equations |
| title_sort | theory of causal differential equations |
| topic | Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020621534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV036703056 |
| work_keys_str_mv | AT lakshmikanthamvangipuram theoryofcausaldifferentialequations |