Introduction to linear systems of differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1995
|
| Series: | Translations of mathematical monographs
146 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 204 S. |
| ISBN: | 082180328X |
Staff View
MARC
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| 100 | 1 | |a Adrianova, L. Ja. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Vvedenie v teoriju linejnych sistem differencial'nych uravnenij |
| 245 | 1 | 0 | |a Introduction to linear systems of differential equations |c L. Ya. Adrianova |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1995 | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
Principal Notation ix
Chapter I. Linear Autonomous and Periodic Systems 1
§ 1. Adjoint systems 2
§2. The matriciant and its properties 3
§3. Linear systems with constant coefficients 8
§4. Homogeneous systems with periodic coefficients. The Floquet theorem 13
§5. Nonhomogeneous periodic systems 20
Chapter II. Lyapunov Characteristic Exponents in the Theory of Linear Systems 25
§1. Definition and main properties of characteristic exponents 25
§2. Characteristic exponents of matrices of functions 31
§3. The spectrum of a linear system 33
§4. Normal fundamental systems or normal bases 35
§5. The Lyapunov inequality for the sum of characteristic exponents of bases 40
Chapter III. Reducible, Almost Reducible, and Regular Systems 43
§ 1. Lyapunov transformations 43
§2. Reducible systems 45
§3. Reduction of a linear system to a triangular or a block triangular form 48
§4. Almost reducible systems 57
§5. Regular systems 60
§6. Perron s regularity test. Coefficients of irregularity 63
§7. The structure of fundamental matrices of a regular system. Generalized
reducibility 68
§8. Regularity of a triangular system 72
§9. Properties of solutions of regular systems 75
Chapter IV. Stability and Small Perturbations of the Coefficients of Linear Sys¬
tems 79
§ 1. On stability of linear systems 79
§2. On stability of linear homogeneous sytems whose coefficients are constant,
periodic, or satisfy the Lappo Danilevskii condition 84
§3. Almost constant systems 88
§4. Uniformly stable and uniformly asymptotically stable linear systems 95
§5. On perturbations preserving the spectrum of a system. The principle of
linear inclusion 104
y
vi CONTENTS
§6. Growth estimates of the solutions of linear systems in terms of the coeffi¬
cients 108
Chapter V. On the Variation of Characteristic Exponents Under Small Pertur¬
bations of Coefficients 121
§1. Central exponents 122
§2. On the stability of characteristic exponents 136
§3. Integral separateness 146
§4. Necessary and sufficient conditions for stability of characteristic expo¬
nents 153
Chapter VI. A Linear Homogeneous Equation of the Second Order 175
§ 1. On the oscillation of solutions of a linear homogeneous equation of the
second order 176
§2. On boundedness and stability of solutions of a linear equation of the
second order 185
§3. Linear equations with periodic coefficients 190
Appendix 197
1. The Gronwall Bellman lemma and its generalization 197
2. Regularity of a linear system almost reducible to an autonomous one 198
References 201
Index 203
|
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| indexdate | 2024-07-09T17:57:24Z |
| institution | BVB |
| isbn | 082180328X |
| language | English Russian |
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| physical | X, 204 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Adrianova, L. Ja. Verfasser aut Vvedenie v teoriju linejnych sistem differencial'nych uravnenij Introduction to linear systems of differential equations L. Ya. Adrianova Providence, RI American Math. Soc. 1995 X, 204 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 146 Aus dem Russ. übers. Equations différentielles linéaires ram Differential equations, Linear Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 s DE-604 Translations of mathematical monographs 146 (DE-604)BV000002394 146 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Adrianova, L. Ja Introduction to linear systems of differential equations Translations of mathematical monographs Equations différentielles linéaires ram Differential equations, Linear Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| subject_GND | (DE-588)4206889-7 |
| title | Introduction to linear systems of differential equations |
| title_alt | Vvedenie v teoriju linejnych sistem differencial'nych uravnenij |
| title_auth | Introduction to linear systems of differential equations |
| title_exact_search | Introduction to linear systems of differential equations |
| title_full | Introduction to linear systems of differential equations L. Ya. Adrianova |
| title_fullStr | Introduction to linear systems of differential equations L. Ya. Adrianova |
| title_full_unstemmed | Introduction to linear systems of differential equations L. Ya. Adrianova |
| title_short | Introduction to linear systems of differential equations |
| title_sort | introduction to linear systems of differential equations |
| topic | Equations différentielles linéaires ram Differential equations, Linear Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| topic_facet | Equations différentielles linéaires Differential equations, Linear Lineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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