Oscillation theory of two-term differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1997
|
| Series: | Mathematics and its application
396 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 217 S. |
| ISBN: | 0792344472 |
Staff View
MARC
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| 300 | |a VII, 217 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE vii
0. INTRODUCTION 1
0.1 Linear differential equations and disconjugacy 1
0.2 Polya s factorization 3
0.3 Willet s notation 7
0.4 Green s function 8
1. THE BASIC LEMMA 11
1.1 Two term equations 11
1.2 The basic lemma 12
1.3 Examples 21
2. BOUNDARY VALUE FUNCTIONS 27
2.1 Boundary value functions 27
2.2 More boundary value problems 31
2.3 Extremal points and boundary value problems 32
3. BASES OF SOLUTIONS 42
3.1 A base of solutions 42
3.2 Adjoint equations and boundary value problems 45
4. COMPARISON OF BOUNDARY VALUE PROBLEMS 49
4.1 Ordering of boundary value problems 49
4.2 m poised boundary value problems 55
4.3 Comparison of Green s functions 57
5. COMPARISON THEOREMS FOR TWO EQUATIONS 60
5.1 Pointwise comparison of coefficients 60
5.2 Integral comparison of coefficients 65
6. DISFOCALITY AND ITS CHARACTERIZATION 67
6.1 Characterization of disfocality 67
6.2 Integral characterization of disfocality 73
6.3 A lemma of Kiguradze 78
6.4 Explicit integral criteria for disfocality 81
6.5 Asymptotic behaviour of solutions 87
6.6 Euler s equation and disfocality 91
6.7 Green s function of the focal boundary value problem 95
7. VARIOUS TYPES OF DISFOCALITY 98
7.1 Comparison of various types of disfocality 98
7.2 Application to the equation j/ +py = 0 105
7.3 Comparison theorems with integrated coefficients 107
8. SOLUTIONS ON AN INFINITE INTERVAL Ill
8.1 A classification of the solutions Ill
8.2 Nonoscillation and eventual disconjugacy 120
8.3 Equivalence of disconjugacy and disfocality 121
v
vi CONTENTS
8.4 The limit of Green s functions 124
8.5 Property A, Property B and strong oscillation 126
8.6 Nonoscillation 129
9. DISCONJUGACY AND ITS CHARACTERIZATION 131
9.1 Disconjugacy and disfocality 131
9.2 Characterization of (k, n fc) disconjugacy 133
9.3 Explicit criteria for disconjugacy 136
9.4 A transformation of the equation 139
10. EIGENVALUE PROBLEMS 141
10.1 Existence of eigenvalues 141
10.2 Zeros of eigenfunctions 146
10.3 Dependence on the boundary conditions 152
10.4 Comparison of two point boundary value problems 156
11. MORE EXTREMAL POINTS 161
11.1 The ith conjugate point 161
11.2 The focal point 164
11.3 Maximal gap between zeros 166
12. MINORS OF THE WRONSKIAN 176
12.1 Minors as solutions of a differential equation 176
12.2 Zeros of odd order minors 185
12.3 Applications to oscillation 191
13. THE DOMINANCE PROPERTY OF SOLUTIONS 193
13.1 Dominance 193
13.2 Comparison of minors 200
13.3 Dichotomy of a nonoscillatory set 205
13. REFERENCES 209
13. INDEX 217
|
| any_adam_object | 1 |
| author | Elias, Uri |
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| id | DE-604.BV011568345 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:58Z |
| institution | BVB |
| isbn | 0792344472 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007788662 |
| oclc_num | 36327419 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | VII, 217 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its application |
| series2 | Mathematics and its application |
| spelling | Elias, Uri Verfasser aut Oscillation theory of two-term differential equations by Uri Elias Dordrecht [u.a.] Kluwer Acad. Publ. 1997 VII, 217 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its application 396 Équations différentielles linéaires ram Differential equations, Linear Oscillations Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s DE-604 Mathematics and its application 396 (DE-604)BV008163334 396 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007788662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elias, Uri Oscillation theory of two-term differential equations Mathematics and its application Équations différentielles linéaires ram Differential equations, Linear Oscillations Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| subject_GND | (DE-588)4353441-7 |
| title | Oscillation theory of two-term differential equations |
| title_auth | Oscillation theory of two-term differential equations |
| title_exact_search | Oscillation theory of two-term differential equations |
| title_full | Oscillation theory of two-term differential equations by Uri Elias |
| title_fullStr | Oscillation theory of two-term differential equations by Uri Elias |
| title_full_unstemmed | Oscillation theory of two-term differential equations by Uri Elias |
| title_short | Oscillation theory of two-term differential equations |
| title_sort | oscillation theory of two term differential equations |
| topic | Équations différentielles linéaires ram Differential equations, Linear Oscillations Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| topic_facet | Équations différentielles linéaires Differential equations, Linear Oscillations Lineare gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007788662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT eliasuri oscillationtheoryoftwotermdifferentialequations |