Non-linear differential equations of higher order:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Leyden
Noordhoff International Publishing
1974
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 669 Seiten 23 cm |
| ISBN: | 9001752705 |
Staff View
MARC
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| 240 | 1 | 0 | |a Nichtlineare Differentialgleichungen höherer Ordnung |
| 245 | 1 | 0 | |a Non-linear differential equations of higher order |c R. Reissig ; G. Sansone ; R. Conti |
| 264 | 1 | |a Leyden |b Noordhoff International Publishing |c 1974 | |
| 300 | |a XIII, 669 Seiten |c 23 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Équations différentielles non linéaires | |
| 650 | 4 | |a Differential equations, Nonlinear | |
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| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Sansone, Giovanni |d 1888-1979 |e Verfasser |0 (DE-588)11772047X |4 aut | |
| 700 | 1 | |a Conti, Roberto |d 1923-2006 |e Verfasser |0 (DE-588)1025204603 |4 aut | |
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Record in the Search Index
| _version_ | 1804116395485560832 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface ix
Chapter 1
General methods of the qualitative theory
1.1. Some stability theorems 1
1.2. Criteria for boundedness 44
1.3. Periodic solutions of autonomous systems 66
1.4. Existence of periodic solutions in non-autonomous systems 72
References for Chapter 1 123
Chapter 2
Stability and boundedness on the basis of
approximations
2.1. General comparison theorems 131
2.2. Investigations by means of series expansions according to
Lyapunov-Malkin 162
2.2.1. Stability and instability in the m-th approximation
162
2.2.2. The critical cases for certain third and fourth order
systems 173
2.2.3. Transformation of the fundamental equations 176
2.2.4. Case of one vanishing root 179
2.2.5. Case of a pair of purely imaginary roots 180
2.2.6. Case of two vanishing roots (simple elementary divi¬
sors) 183
v
Table of contents
2.2.7. Case of two vanishing roots (twofold elementary divi¬
sor) 190
2.2.8. Extension of the results to systems containing non-
critical variables 194
2.2.9. Application of the theorems to differential equations
of the third and fourth order 201
References for Chapter 2 206
Chapter 3
The behaviour of the trajectories of autonomous
systems
3.1. Linear systems of three equations 216 -
3.1.1. The reduced systems in the non-singular case 216
3.1.2. Behaviour of the trajectories of the reduced systems
218
3.1.3. The singular case 228
3.1.4. Behaviour of the trajectories at infinity 234
3.2. Some examples of non-linear systems of the third order 234
3.2.1. Differential equations of the Jacobi elliptic functions
234
3.2.2. The system of Kasner 236
3.2.3. Examples of Bielecki-Zaremba and others 238
3.3. Behaviour of the trajectories in the neighbourhood of a sin¬
gular point 240
3.3.1. The system of Reizin 240
3.3.2. Exceptional directions 242
3.3.3. Sufficient conditions for a stellar node 244
3.3.4. Case of an isolated exceptional direction 250
3.4. Behaviour of the trajectories in the neighbourhood of a limit
cycle 254
3.5. The trajectories of an autonomous system of n equations 258
References for Chapter 3 261
VI
Table of contents
Chapter 4
The equation of type x + ax + p(x, x ) +f(x) = p(t)
4.1. Stability in the autonomous case [p(t) = 0] 264
4.2. Boundedness and existence of periodic solutions in the non-
autonomous case [p{t) # 0] 287
References for Chapter 4 366
Chapter 5
The equation of type * + iji{x, x )x + p(x ) +/(*) =
= p(t) and other equations
5.1. The autonomous case 369
5.2. The non-autonomous case 401
References for Chapter 5 418
Chapter 6
The equation of type * + /CO* + W* )* +
+ p(x ) +f(x) =p(t) and more general types
6.1. The autonomous case 420
6.2. The non-autonomous case 437
References for Chapter 6 458
Chapter 7
Systems of arbitrary order
Non-linearities with separate variables
7.1. General stability considerations and Aizerman s problem 460
7.2. Stability of some second order systems 470
7.3. Investigations of stability for certain third order systems 504
7.4. Boundedness of the solutions for certain non-autonomous
systems of the third order 553
References for Chapter 7 572
VII
Table of contents
Chapter 8
n-th order systems of Lur e type
8.1. Fundamental equations and statement of the problem 575
8.2. Derivation of sufficient criteria for absolute stability by con¬
struction of Lyapunov functions 588
8.3. Criterion of Popov for absolute stability in the angle [0, k]
for direct control 598
8.4. Criteria of Corduneanu for absolute stability in the case of
indirect control 612
8.5. Connection of the criteria of Popov with the existence of
certain Lyapunov functions 631
8.5.1. The principal case and the simplest singular case 631 ..
8.5.2. Some inequalities for matrices 638
References for Chapter 8 658
Subject index 665
VTII
|
| any_adam_object | 1 |
| author | Reißig, Rolf 1922- Sansone, Giovanni 1888-1979 Conti, Roberto 1923-2006 |
| author_GND | (DE-588)136718140 (DE-588)11772047X (DE-588)1025204603 |
| author_facet | Reißig, Rolf 1922- Sansone, Giovanni 1888-1979 Conti, Roberto 1923-2006 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:50Z |
| institution | BVB |
| isbn | 9001752705 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001273657 |
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| physical | XIII, 669 Seiten 23 cm |
| publishDate | 1974 |
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| publishDateSort | 1974 |
| publisher | Noordhoff International Publishing |
| record_format | marc |
| spelling | Reißig, Rolf 1922- Verfasser (DE-588)136718140 aut Nichtlineare Differentialgleichungen höherer Ordnung Non-linear differential equations of higher order R. Reissig ; G. Sansone ; R. Conti Leyden Noordhoff International Publishing 1974 XIII, 669 Seiten 23 cm txt rdacontent n rdamedia nc rdacarrier Équations différentielles non linéaires Differential equations, Nonlinear Ordnung n (DE-588)4322729-6 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s DE-604 Differentialgleichung (DE-588)4012249-9 s Ordnung n (DE-588)4322729-6 s 1\p DE-604 Sansone, Giovanni 1888-1979 Verfasser (DE-588)11772047X aut Conti, Roberto 1923-2006 Verfasser (DE-588)1025204603 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001273657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reißig, Rolf 1922- Sansone, Giovanni 1888-1979 Conti, Roberto 1923-2006 Non-linear differential equations of higher order Équations différentielles non linéaires Differential equations, Nonlinear Ordnung n (DE-588)4322729-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4322729-6 (DE-588)4205536-2 (DE-588)4012249-9 |
| title | Non-linear differential equations of higher order |
| title_alt | Nichtlineare Differentialgleichungen höherer Ordnung |
| title_auth | Non-linear differential equations of higher order |
| title_exact_search | Non-linear differential equations of higher order |
| title_full | Non-linear differential equations of higher order R. Reissig ; G. Sansone ; R. Conti |
| title_fullStr | Non-linear differential equations of higher order R. Reissig ; G. Sansone ; R. Conti |
| title_full_unstemmed | Non-linear differential equations of higher order R. Reissig ; G. Sansone ; R. Conti |
| title_short | Non-linear differential equations of higher order |
| title_sort | non linear differential equations of higher order |
| topic | Équations différentielles non linéaires Differential equations, Nonlinear Ordnung n (DE-588)4322729-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Équations différentielles non linéaires Differential equations, Nonlinear Ordnung n Nichtlineare Differentialgleichung Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001273657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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