Gespeichert in:
| Titel: | Systems of evolution equations with periodic and quasiperiodic coefficients |
|---|---|
| Von: |
by Yu. A. Mitropolsky, A. M. Samoilenko and D. I. Martinyuk
|
| Person: |
Mitropolʹskij, Jurij Alekseevič
1917-2008 Verfasser aut Samojlenko, Anatolij M. Martinyuk, D. I. 1938-2020 |
| Hauptverfassende: | , , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Schriftenreihe: | Mathematics and its applications
87 |
| Schlagworte: | |
| Online-Zugang: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288575&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | XIV, 280 S. |
| ISBN: | 0792320549 |
Internformat
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| 100 | 1 | |a Mitropolʹskij, Jurij Alekseevič |d 1917-2008 |e Verfasser |0 (DE-588)104890029 |4 aut | |
| 245 | 1 | 0 | |a Systems of evolution equations with periodic and quasiperiodic coefficients |c by Yu. A. Mitropolsky, A. M. Samoilenko and D. I. Martinyuk |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a XIV, 280 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications / Soviet series |v 87 | |
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| 650 | 0 | 7 | |a Quasiperiodische Lösung |0 (DE-588)4236468-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Samojlenko, Anatolij M. |d 1938-2020 |e Verfasser |0 (DE-588)108416569 |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 94 A 1373 |
|---|---|
| DE-BY-TUM_katkey | 596821 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040000798169 |
| _version_ | 1821938807664017408 |
| adam_text | CONTENTS
Preface xi
CHAPTER 1. NUMERICAL ANALYTIC METHOD OF
INVESTIGATION OF PERIODIC SOLUTIONS
FOR SYSTEMS WITH AFTEREFFECT 1
§1. Notations and Basic Ideas. Auxiliary Lemmas 2
§2. Algorithm for Finding Periodic Solutions of Nonlinear Systems with Lag 6
§3. Existence of Periodic Solutions 13
§4. Construction of an Approximate Periodic Solution 18
§5. Periodic Problem of Control for Systems with Lag 26
§6. The Concrete Example of Application of the Numerical Analytic Method 27
§7. Periodic Solutions of Differential Equations of the Second Order with
Retarded Argument 30
§8. Periodic Solutions for Countable Systems of Differential Equations
with Lag 38
§9. Periodic Solutions for Nonlinear Systems of Differential Equations
of the Neutral Type 42
§ 10. Investigation of Periodic Solutions for Some Classes of Systems of
Integro Differential Equations 45
§11. Periodic Solutions of Nonlinear Systems of Difference Equations 55
§ 12. Bilateral Approximations to Periodic Solutions of Systems with Lag 59
§13. Periodic Solutions of Operator Differential Equations 71
CHAPTER 2. INVESTIGATION OF PERIODIC SOLUTIONS OF
SYSTEMS WITH AFTEREFFECT BY BUBNOV
GALERKIN S METHOD 77
§1. Preliminary Remarks. Auxiliary Statements 77
§2. Green s Function for the Problem of Periodic Solutions of Linear
Systems with Lag. Properties of This Function 83
§3. The Main Properties of the Jacobian Matrix for Determining
Equations for Galerkin s Approximations 87
vii
viii Contents
§4. Existence and Convergence of Bubnov Galerkin s Approximations 93
§5. Existence of Periodic Solutions for Systems of Differential Equations
with Lag 98
§6. Applications of Bubnov Galerkin s Method to the Investigation
of Periodic Solutions for Some Classes of Systems of Integro
Differential Equations 101
CHAPTER 3.QUASIPERIODIC SOLUTIONS OF SYSTEMS
WITH LAG. BUBNOV GALERKIN S METHOD 107
§1. Definitions and Auxiliary Statements 107
§2. Construction of Quasiperiodic Solutions of Systems with Lag by
Bubnov Galerkin s Method 114
§3. Construction of Quasiperiodic Solutions of Perturbed Systems with
Lag by Bubnov Galerkin s Method 123
CHAPTER 4. EXISTENCE OF INVARIANT TOROIDAL MANI¬
FOLDS FOR SYSTEMS WITH LAG. INVESTIGA¬
TION OF THE BEHAVIOR OF TRAJECTORIES
IN THEIR VICINITIES 135
§1. Existence of Invariant Toroidal Manifolds with Loss of Smoothness 135
§2. Existence of Lipschitz Tori for Nonlinear Systems with Lag 150
§3. Invariant Toroidal Sets for the Systems of Differential Equations
with Lag Under Pulse Influence 169
§4. Behavior of Solutions of Nonlinear Systems with Lag in the Vicinity
of Exponentially Stable Toroidal Manifolds 185
CHAPTER 5. REDUCIBILITY OF LINEAR SYSTEMS OF
DIFFERENCE EQUATIONS WITH QUASI
PERIODIC COEFFICIENTS 201
§1. Statement of the Problem and Auxiliary Statements 201
§2. Theorem on Reducibility 206
§3. Reducibility of Linear Systems of Difference Equations with a
Smooth Right Hand Side 214
Contents ix
CHAPTER 6. INVARIANT TOROIDAL SETS FOR SYSTEMS OF
DIFFERENCE EQUATIONS. INVESTIGATION OF
THE BEHAVIOR OF TRAJECTORIES ON TOROI¬
DAL SETS AND IN THEIR VICINITIES 223
§1. Auxiliary Lemmas 223
§2. Periodic Solutions to Some Classes of Functional Equations 229
§3. Existence of Invariant Toroidal Sets for Nonlinear Systems of
Difference Equations 236
§4. Reducibility of Systems of Difference Equations on the Toroidal Set 245
§5. Reducibility of Nonlinear Systems of Difference Equations in the
Vicinity of the Toroidal Set 253
References 263
Index 279
|
| any_adam_object | 1 |
| author | Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 Martinyuk, D. I. |
| author_GND | (DE-588)104890029 (DE-588)108416569 |
| author_facet | Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 Martinyuk, D. I. |
| author_role | aut aut aut |
| author_sort | Mitropolʹskij, Jurij Alekseevič 1917-2008 |
| author_variant | j a m ja jam a m s am ams d i m di dim |
| building | Verbundindex |
| bvnumber | BV008038410 |
| classification_rvk | SK 540 |
| classification_tum | MAT 354f |
| ctrlnum | (OCoLC)246570331 (DE-599)BVBBV008038410 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008038410 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:15:23Z |
| institution | BVB |
| isbn | 0792320549 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005288575 |
| oclc_num | 246570331 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-188 |
| physical | XIV, 280 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spellingShingle | Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 Martinyuk, D. I. Systems of evolution equations with periodic and quasiperiodic coefficients Evolutionsgleichung (DE-588)4129061-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Quasiperiodische Lösung (DE-588)4236468-1 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4199269-6 (DE-588)4236468-1 |
| title | Systems of evolution equations with periodic and quasiperiodic coefficients |
| title_auth | Systems of evolution equations with periodic and quasiperiodic coefficients |
| title_exact_search | Systems of evolution equations with periodic and quasiperiodic coefficients |
| title_full | Systems of evolution equations with periodic and quasiperiodic coefficients by Yu. A. Mitropolsky, A. M. Samoilenko and D. I. Martinyuk |
| title_fullStr | Systems of evolution equations with periodic and quasiperiodic coefficients by Yu. A. Mitropolsky, A. M. Samoilenko and D. I. Martinyuk |
| title_full_unstemmed | Systems of evolution equations with periodic and quasiperiodic coefficients by Yu. A. Mitropolsky, A. M. Samoilenko and D. I. Martinyuk |
| title_short | Systems of evolution equations with periodic and quasiperiodic coefficients |
| title_sort | systems of evolution equations with periodic and quasiperiodic coefficients |
| topic | Evolutionsgleichung (DE-588)4129061-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Quasiperiodische Lösung (DE-588)4236468-1 gnd |
| topic_facet | Evolutionsgleichung Periodische Lösung Quasiperiodische Lösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288575&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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