Theory of a higher order Sturm-Liouville equation:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1659 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 140 S. |
| ISBN: | 3540630651 |
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MARC
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Record in the Search Index
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| adam_text |
VLADIMIR KOZLOV VLADIMIR MAZ'YA THEORY OF A HIGHER-ORDER STURM-LIOUVILLE
EQUATION WK SPRINGER TABLE OF CONTENTS INTRODUCTION V 1. BASIC EQUATION
WITH CONSTANT COEFFICIENTS 1 1.1 INTRODUCTION 1 1.2 GREEN'S FUNCTION FOR
M(D T ) ON R 2 1.3 NECESSARY AND SUFFICIENT CONDITION FOR SOLVABILITY 4
1.4 NECESSARY AND SUFFICIENT CONDITION FOR POWER-EXPONENTIAL ASYMPTOTICS
8 1.5 A LARGER CLASS OF ORDINARY DIFFERENTIAL EQUATIONS 12 2. THE
OPERATOR M(D T ) ON A SEMIAXIS AND AN INTERVAL 15 2.1 INTRODUCTION 15
2.2 PROPERTIES OF GREEN'S FUNCTION 15 2.3 UNIQUE SOLVABILITY OF THE
BOUNDARY VALUE PROBLEM ON A SEMI- AXIS 17 2.4 ASYMPTOTICS AT INFINITY 18
2.5 UNIQUE SOLVABILITY OF THE BOUNDARY VALUE PROBLEM ON A FINITE
INTERVAL 20 2.6 POSITIVITY OF POISSON'S FUNCTIONS 21 2.7 GREEN'S
FUNCTION FOR THE BOUNDARY VALUE PROBLEM ON AN IN- TERVAL 21 2.8
POSITIVITY OF GREEN'S FUNCTION 23 3. THE OPERATOR M(DT) * UQ WITH
CONSTANT WO 2 5 3.1 INTRODUCTION 25 3.2 ROOTS OF THE CHARACTERISTIC
EQUATION 26 3.3 GREEN'S FUNCTION FOR M(D T ) - 0 ONR 28 3.4 UNIQUENESS
AND SOLVABILITY 31 3.5 STABLE ESTIMATE 34 4. GREEN'S FUNCTION FOR THE
OPERATOR M{D T ) - U{T) 37 4.1 PROPERTIES OF GREEN'S FUNCTION 37 4.2
MONOTONICITY PROPERTIES OF GREEN'S FUNCTION WITH RESPECT TO W 39 X TABLE
OF CONTENTS 4.3 MULTIPLICATIVE ESTIMATE FOR GREEN'S FUNCTION AND ITS
DERIVATIV 4.4 OTHER ESTIMATES FOR GREEN'S FUNCTION 43 5. UNIQUENESS AND
SOLVABILITY PROPERTIES OF THE OPERATOR M (DT) * U(T) 47 5.1 INTRODUCTION
47 5.2 EXISTENCE THEOREM AND PROPERTIES OF SOLUTIONS 48 5.3 THE EQUATION
ON A BOUNDED INTERVAL 52 5.4 UNIQUENESS 55 5.5 SOME COROLLARIES OF THE
UNIQUENESS THEOREM 61 5.6 THE BOUNDARY VALUE PROBLEM ON A SEMIAXIS 63
5.7 REPRESENTATION FOR G U 67 5.8 PROPERTIES OF G U AND UNIQUENESS
THEOREM WHEN M+ = 1 OR M_ = 1 72 5.9 THE SPACE X+(W) FOR M+ = 2 73 5.10
GREEN'S FUNCTION AND UNIQUENESS THEOREM WHEN M+ = 2. 77 5.11 THE
SPACE X-(U) FOR M_ = 2 78 6. PROPERTIES OF M(8 T ) * W(T) UNDER VARIOUS
ASSUMPTIONS ABOUT U)(T) 81 6.1 INTRODUCTION 81 6.2 THE CASE OF BOUNDED
COEFFICIENT U 84 6.3 THE CASE OF SUMMABLE U 86 6.4 THE CASE M+ = M_ = 1
90 6.5 UNIQUENESS AND SOLVABILITY IN THE CASE M+ = M_ = 1 93 6.6 POWER
PERTURBATION (ESTIMATES FOR G U IN THE CASE A M + ) . 94 6.7 POWER
PERTURBATION (ESTIMATES FOR G U IN THE CASE A = M+) . 98 6.8 POWER
PERTURBATION (UNIQUENESS AND SOLVABILITY) 100 6.9 ESTIMATES FOR G W WHEN
W 'DOMINATES' EITHER T~ M+ OR T~ M - FOR LARGE POSITIVE T 101 6.10
UNIQUENESS AND EXISTENCE THEOREMS IN THE CASE (W _1 / M -)' - 0 110 7.
ASYMPTOTICS OF SOLUTIONS AT INFINITY 111 7.1 ESTIMATES FOR GREEN'S
FUNCTION G U UNDER THE ASSUMPTION OF WEIGHTED SUMMABILITY OF U(T) 111
7.1.1 STATEMENT OF THE RESULT 111 7.1.2 PROOF OF THEOREM 7.1.1 112 7.1.3
REMARKS AND COROLLARIES 116 7.2 AUXILIARY EXISTENCE ASSERTIONS 118 7.3
ASYMPTOTICS OF SOLUTIONS OF THE HOMOGENEOUS EQUATION 121 7.4 NECESSARY
AND SUFFICIENT CONDITION FOR ASYMPTOTICS 124 TABLE OF CONTENTS XI A.
APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS WITH OPER- ATOR
COEFFICIENTS 127 A.L COMPARISON PRINCIPLE FOR EQUATIONS WITH CONSTANT
OPERATOR COEFFICIENTS 127 A.2 COMPARISON PRINCIPLE FOR EQUATIONS WITH
VARIABLE OPERATOR COEFFICIENTS 130 A.3 SOME SPECIAL CASES 132 A.3.1 THE
CASE M+ = M_ = 1 132 A.3.2 POWER PERTURBATIONS 133 A.4 POWER-EXPONENTIAL
ASYMPTOTICS OF SOLUTIONS TO THE OPERATOR EQUATION WITH VARIABLE
COEFFICIENTS 134 REFERENCES 137 INDEX 139 |
| any_adam_object | 1 |
| author | Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- |
| author_GND | (DE-588)103679014 (DE-588)121490602 |
| author_facet | Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- |
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| ctrlnum | (OCoLC)36922507 (DE-599)BVBBV011341986 |
| dewey-full | 515/.352 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.352 510 |
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| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011341986 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-15T08:01:01Z |
| institution | BVB |
| isbn | 3540630651 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007621006 |
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| physical | XI, 140 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Kozlov, Vladimir 1954- Verfasser (DE-588)103679014 aut Theory of a higher order Sturm-Liouville equation V. Kozlov and V. Maz'ya Berlin [u.a.] Springer 1997 XI, 140 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1659 Asymptotische analyse gtt Equacoes diferenciais larpcal Sturm-Liouville, Équation de Sturm-Liouville, Équation de ram Sturm-Liouville equation Sturm-Liouville-Differentialgleichung (DE-588)4202273-3 gnd rswk-swf Sturm-Liouville-Differenzengleichung (DE-588)4202274-5 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Sturm-Liouville-Differenzengleichung (DE-588)4202274-5 s DE-604 Sturm-Liouville-Differentialgleichung (DE-588)4202273-3 s Ordnung n (DE-588)4322729-6 s Mazʹja, Vladimir Gilelevič 1937- Verfasser (DE-588)121490602 aut Lecture notes in mathematics 1659 (DE-604)BV000676446 1659 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007621006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- Theory of a higher order Sturm-Liouville equation Lecture notes in mathematics Asymptotische analyse gtt Equacoes diferenciais larpcal Sturm-Liouville, Équation de Sturm-Liouville, Équation de ram Sturm-Liouville equation Sturm-Liouville-Differentialgleichung (DE-588)4202273-3 gnd Sturm-Liouville-Differenzengleichung (DE-588)4202274-5 gnd Ordnung n (DE-588)4322729-6 gnd |
| subject_GND | (DE-588)4202273-3 (DE-588)4202274-5 (DE-588)4322729-6 |
| title | Theory of a higher order Sturm-Liouville equation |
| title_auth | Theory of a higher order Sturm-Liouville equation |
| title_exact_search | Theory of a higher order Sturm-Liouville equation |
| title_full | Theory of a higher order Sturm-Liouville equation V. Kozlov and V. Maz'ya |
| title_fullStr | Theory of a higher order Sturm-Liouville equation V. Kozlov and V. Maz'ya |
| title_full_unstemmed | Theory of a higher order Sturm-Liouville equation V. Kozlov and V. Maz'ya |
| title_short | Theory of a higher order Sturm-Liouville equation |
| title_sort | theory of a higher order sturm liouville equation |
| topic | Asymptotische analyse gtt Equacoes diferenciais larpcal Sturm-Liouville, Équation de Sturm-Liouville, Équation de ram Sturm-Liouville equation Sturm-Liouville-Differentialgleichung (DE-588)4202273-3 gnd Sturm-Liouville-Differenzengleichung (DE-588)4202274-5 gnd Ordnung n (DE-588)4322729-6 gnd |
| topic_facet | Asymptotische analyse Equacoes diferenciais Sturm-Liouville, Équation de Sturm-Liouville equation Sturm-Liouville-Differentialgleichung Sturm-Liouville-Differenzengleichung Ordnung n |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007621006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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