Availability: Theory of a higher order Sturm-Liouville equation

Theory of a higher order Sturm-Liouville equation:

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Bibliographic Details
Main Authors:	Kozlov, Vladimir 1954- (Author), Mazʹja, Vladimir Gilelevič 1937- (Author)
Format:	Book
Language:	German
Published:	Berlin [u.a.] Springer 1997
Series:	Lecture notes in mathematics 1659
Subjects:	Asymptotische analyse Equacoes diferenciais Sturm-Liouville, Équation de Sturm-Liouville equation Sturm-Liouville-Differentialgleichung Sturm-Liouville-Differenzengleichung Ordnung n
Links:	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
Physical Description:	XI, 140 S.
ISBN:	3540630651

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245	1	0	\|a Theory of a higher order Sturm-Liouville equation \|c V. Kozlov and V. Maz'ya
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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
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author	Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937-
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author_facet	Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937-
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indexdate	2025-04-15T08:00:58Z
institution	BVB
isbn	3540630651
language	German
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physical	XI, 140 S.
publishDate	1997
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publisher	Springer
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series	Lecture notes in mathematics
series2	Lecture notes in mathematics
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
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT kozlovvladimir theoryofahigherordersturmliouvilleequation AT mazʹjavladimirgilelevic theoryofahigherordersturmliouvilleequation

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