Asymptotic properties of solutions of nonautonomous ordinary differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Academic Publishers
1993
|
| Series: | Mathematics and Its Applications / Soviet Series
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt |
| Physical Description: | XIV, 331 Seiten |
| ISBN: | 079232059X |
Staff View
MARC
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| 100 | 1 | |a Kiġuraje, I. T. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Asimptotičeskie svojstva rešenij neavtonomnych obyknovennych differencial'nych uravnenij |
| 245 | 1 | 0 | |a Asymptotic properties of solutions of nonautonomous ordinary differential equations |c by I. T. Kiguradze, Institute of Applied Mathematics, Tblisi, Georgia, and T. A. Chanturia† |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Academic Publishers |c 1993 | |
| 300 | |a XIV, 331 Seiten | ||
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| 490 | 1 | |a Mathematics and Its Applications / Soviet Series |v 89 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Series Editor s preface v
Preface xi
Basic Notation xiii
Chapter I. LINEAR DIFFERENTIAL EQUATIONS 1
§1. Equations Having Properties A and B 1
1.1. Classification of nonoscillatory solutions 2
1.2. Conjugate points of the equation (1.1) 12
1.3. Necessary and sufficient conditions for the equation (1.1) to have prop¬
erties A and B 20
1.4. Integral criteria for the equation (1.1) to have properties A and B 25
1.5. On general equations 30
Notes 41
§2. Oscillatory and Nonoscillatory Equations 42
2.1. Some auxiliary assertions 43
2.2. Oscillation and nonoscillation criteria 52
2.3. On third, fourth and sixth order equations 57
Notes 67
§3. Oscillation Properties of Solutions of Equations with Strongly Os¬
cillating Coefficients 68
3.1. Zeros of solutions on a finite interval 68
3.2. Oscillation of all solutions of equations with strongly oscillating coefficients 74
Notes 76
§4. The Subspace of Solutions Vanishing at Infinity 76
4.1. Some integral identities and inequalities 77
4.2. On functions satisfying the conditions (4.19) 81
4.3. On a related problem 82
4.4. Theorems on the dimension of the space V^n a po,... ,pn i) 84
4.5. Theorems on the dimension of the space V^n p) 89
4.6. On solutions of second order equations 96
Notes 106
vii
viii CONTENTS
§5. Bounded and Unbounded Solutions 106
5.1. Inequalities of Kolmogorov Gorny type 107
5.2. Lemmas on the solvability of related boundary value problems 109
5.3. On the space BM(p) 112
5.4. Existence theorems for unbounded oscillatory solutions 118
5.5. On second order equations 126
Notes 128
§6. Asymptotic Formulas 128
6.1. Statement of the main theorem 128
6.2. Auxiliary assertions 129
6.3. Proof of the main theorem 131
6.4. Equations with almost constant coefficients 134
6.5. Equations with asymptotically small coefficients 135
6.6. Equations asymptotically equivalent to two term ones 136
Notes 143
Chapter II. QUASILINEAR DIFFERENTIAL EQUATIONS 145
§7. Statement of the Problem. Auxiliary Assertions 145
7.1. Linear equations having the Levinson property 147
7.2. On a system of nonlinear integral equations 150
§8. The Family of Ch Type Solutions of the Equation (7.1) 152
8.1. Necessary and sufficient conditions for the existence of Ch type solutions 152
8.2. Asymptotic representations for solutions of a related differential inequality 162
8.3. Stability of the family of Ch type solutions 163
Notes 169
§9. C°h, ££° and Ch Type Equations 169
9.1. Lemmas on integral inequalities 169
9.2. C°h type equations 171
9.3. ££ type equations 173
9.4. Ch type equations 176
Notes 178
Chapter III. GENERAL NONLINEAR DIFFERENTIAL
EQUATIONS 179
§10. Theorems on the Classification of Equations with Respect to
Their Oscillation Properties 179
10.1. Comparison theorem 180
10.2. Equations having property A or B 184
10.3. Equations having property Ak, Bk, A*k, or B£ 194
Notes 198
CONTENTS ix
§11. Singular Solutions 198
11.1. Nonoscillatory first kind singular solutions 199
11.2. Nonoscillatory second kind singular solutions 202
11.3. Nonexistence theorem for singular solutions 205
Notes 207
§12. Fast Growing Solutions 207
12.1. Existence theorem 207
12.2. Asymptotic estimates 210
Notes 212
§13. Kneser Solutions 212
13.1. Existence theorem 213
13.2. Kneser solutions vanishing at infinity 215
Notes 220
§14. Proper Oscillatory Solutions 220
14.1. Existence theorems 221
14.2. Proper oscillatory solutions vanishing at infinity 229
Notes 234
Chapter IV. HIGHER ORDER DIFFERENTIAL EQUATIONS
OF EMDEN FOWLER TYPE 235
§15. Oscillatory Solutions 235
15.1. Classification of equations with respect to their oscillation properties 235
15.2. Existence of proper oscillatory solutions 236
15.3. Proper oscillatory solutions vanishing at infinity 237
15.4. Oscillatory first kind singular solutions 238
Notes 242
§16. Nonoscillatory Solutions 242
16.1. Kneser solutions 242
16.2. Solutions with power asymptotics 245
16.3. Fast growing solutions 246
16.4. Second kind singular solutions 247
Notes 248
Chapter V. SECOND ORDER DIFFERENTIAL EQUATIONS
OF EMDEN FOWLER TYPE 249
§17. Existence Theorems for Proper and Singular Solutions 249
17.1. Existence of proper solutions 249
17.2. Existence of nonoscillatory singular solutions 251
17.3. Existence of oscillatory singular solutions 254
Notes 256
x CONTENTS
§18. Oscillation and Nonoscillation Criteria for Proper Solutions 256
18.1. Oscillation of all proper solutions 256
18.2. Existence of at least one oscillatory proper solution 261
18.3. Nonoscillation of all proper solutions 263
Notes 265
§19. Unbounded and Bounded Solutions. Solutions Vanishing at
Infinity 265
19.1. Bounded solutions 266
19.2. Solutions vanishing at infinity 266
19.3. Unbounded oscillatory solutions 269
Notes 270
§20. Asymptotic Formulas 270
20.1 Asymptotic representations for oscillatory solutions 270
20.2. Auxiliary assertions 276
20.3. Asymptotic representations for nonoscillatory solutions (the case of a
negative coefficient) 287
20.4. Asymptotic representations for nonoscillatory solutions (the case of a
positive coefficient) 295
20.5. Asymptotic representations for nonoscillatory singular solutions 303
Notes 305
REFERENCES 307
AUTHOR INDEX 329
SUBJECT INDEX 331
|
| any_adam_object | 1 |
| author | Kiġuraje, I. T. Čanturija, Tejmuraz Ambros'evič |
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| bvnumber | BV008038441 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:13:19Z |
| institution | BVB |
| isbn | 079232059X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005288602 |
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| physical | XIV, 331 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Academic Publishers |
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| series2 | Mathematics and Its Applications / Soviet Series |
| spelling | Kiġuraje, I. T. Verfasser aut Asimptotičeskie svojstva rešenij neavtonomnych obyknovennych differencial'nych uravnenij Asymptotic properties of solutions of nonautonomous ordinary differential equations by I. T. Kiguradze, Institute of Applied Mathematics, Tblisi, Georgia, and T. A. Chanturia† Dordrecht [u.a.] Kluwer Academic Publishers 1993 XIV, 331 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematics and Its Applications / Soviet Series 89 Aus dem Russischen übersetzt Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s DE-604 Čanturija, Tejmuraz Ambros'evič Verfasser (DE-588)172545722 aut Soviet Series Mathematics and Its Applications 89 (DE-604)BV004708148 89 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kiġuraje, I. T. Čanturija, Tejmuraz Ambros'evič Asymptotic properties of solutions of nonautonomous ordinary differential equations Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4134367-0 (DE-588)4020929-5 |
| title | Asymptotic properties of solutions of nonautonomous ordinary differential equations |
| title_alt | Asimptotičeskie svojstva rešenij neavtonomnych obyknovennych differencial'nych uravnenij |
| title_auth | Asymptotic properties of solutions of nonautonomous ordinary differential equations |
| title_exact_search | Asymptotic properties of solutions of nonautonomous ordinary differential equations |
| title_full | Asymptotic properties of solutions of nonautonomous ordinary differential equations by I. T. Kiguradze, Institute of Applied Mathematics, Tblisi, Georgia, and T. A. Chanturia† |
| title_fullStr | Asymptotic properties of solutions of nonautonomous ordinary differential equations by I. T. Kiguradze, Institute of Applied Mathematics, Tblisi, Georgia, and T. A. Chanturia† |
| title_full_unstemmed | Asymptotic properties of solutions of nonautonomous ordinary differential equations by I. T. Kiguradze, Institute of Applied Mathematics, Tblisi, Georgia, and T. A. Chanturia† |
| title_short | Asymptotic properties of solutions of nonautonomous ordinary differential equations |
| title_sort | asymptotic properties of solutions of nonautonomous ordinary differential equations |
| topic | Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Asymptotisches Lösungsverhalten Gewöhnliche Differentialgleichung |
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