Differential Equations with Operator Coefficients: with Applications to Boundary Value Problems for Partial Differential Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1999
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | * The aim of this book is to give a self-contained presentation of a theory of ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space. This theory has been developed over the last ten years by the authors. We study equations of the form t L{t, Dt)u{t) := L At-q{t)Dlu{t) = f{t) (0.1) q=O on the real axis lR or semiaxis t > to, where u and f are vector-valued functions and Dt = -i8t. We deal with the following topics • conditions of solvability • classes of uniqueness • estimates for solutions • asymptotic representations of solutions as t ---+ 00 Equations of the form (0.1) have numerous applications, especially to the theory of partial differential equations, and our exposition of abstract results is accompanied by many new applications to this theory. * The roots of the theme treated here are the qualitative and asymp totic theories of linear ordinary differential equations; these date back to Liouville, Sturm, Green, Stokes, Poincare, Lyapunov, to name only a few. In the twentieth century, fundamental contributions to the asymptotic analysis of ordinary differential equations were made by Birkhoff, Perron, Wentzel, Kramers, Brillouin and their numerous successors |
| Beschreibung: | 1 Online-Ressource (XX, 444 p) |
| ISBN: | 9783662115558 9783642084539 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-11555-8 |
Internformat
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| 245 | 1 | 0 | |a Differential Equations with Operator Coefficients |b with Applications to Boundary Value Problems for Partial Differential Equations |c by Vladimir Kozlov, Vladimir Maz’ya |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1999 | |
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| 500 | |a * The aim of this book is to give a self-contained presentation of a theory of ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space. This theory has been developed over the last ten years by the authors. We study equations of the form t L{t, Dt)u{t) := L At-q{t)Dlu{t) = f{t) (0.1) q=O on the real axis lR or semiaxis t > to, where u and f are vector-valued functions and Dt = -i8t. We deal with the following topics • conditions of solvability • classes of uniqueness • estimates for solutions • asymptotic representations of solutions as t ---+ 00 Equations of the form (0.1) have numerous applications, especially to the theory of partial differential equations, and our exposition of abstract results is accompanied by many new applications to this theory. * The roots of the theme treated here are the qualitative and asymp totic theories of linear ordinary differential equations; these date back to Liouville, Sturm, Green, Stokes, Poincare, Lyapunov, to name only a few. In the twentieth century, fundamental contributions to the asymptotic analysis of ordinary differential equations were made by Birkhoff, Perron, Wentzel, Kramers, Brillouin and their numerous successors | ||
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Datensatz im Suchindex
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| author | Kozlov, Vladimir |
| author_facet | Kozlov, Vladimir |
| author_role | aut |
| author_sort | Kozlov, Vladimir |
| author_variant | v k vk |
| building | Verbundindex |
| bvnumber | BV042423454 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)1165526693 (DE-599)BVBBV042423454 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-11555-8 |
| format | Electronic eBook |
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| id | DE-604.BV042423454 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662115558 9783642084539 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (XX, 444 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
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| series2 | Springer Monographs in Mathematics |
| spelling | Kozlov, Vladimir Verfasser aut Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations by Vladimir Kozlov, Vladimir Maz’ya Berlin, Heidelberg Springer Berlin Heidelberg 1999 1 Online-Ressource (XX, 444 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 * The aim of this book is to give a self-contained presentation of a theory of ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space. This theory has been developed over the last ten years by the authors. We study equations of the form t L{t, Dt)u{t) := L At-q{t)Dlu{t) = f{t) (0.1) q=O on the real axis lR or semiaxis t > to, where u and f are vector-valued functions and Dt = -i8t. We deal with the following topics • conditions of solvability • classes of uniqueness • estimates for solutions • asymptotic representations of solutions as t ---+ 00 Equations of the form (0.1) have numerous applications, especially to the theory of partial differential equations, and our exposition of abstract results is accompanied by many new applications to this theory. * The roots of the theme treated here are the qualitative and asymp totic theories of linear ordinary differential equations; these date back to Liouville, Sturm, Green, Stokes, Poincare, Lyapunov, to name only a few. In the twentieth century, fundamental contributions to the asymptotic analysis of ordinary differential equations were made by Birkhoff, Perron, Wentzel, Kramers, Brillouin and their numerous successors Mathematics Differential Equations Ordinary Differential Equations Mathematik Operatorgleichung (DE-588)4043601-9 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s Operatorgleichung (DE-588)4043601-9 s 1\p DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 2\p DE-604 Maz’ya, Vladimir Sonstige oth https://doi.org/10.1007/978-3-662-11555-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kozlov, Vladimir Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations Mathematics Differential Equations Ordinary Differential Equations Mathematik Operatorgleichung (DE-588)4043601-9 gnd Differentialoperator (DE-588)4012251-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4043601-9 (DE-588)4012251-7 (DE-588)4020929-5 |
| title | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations |
| title_auth | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations |
| title_exact_search | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations |
| title_full | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations by Vladimir Kozlov, Vladimir Maz’ya |
| title_fullStr | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations by Vladimir Kozlov, Vladimir Maz’ya |
| title_full_unstemmed | Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations by Vladimir Kozlov, Vladimir Maz’ya |
| title_short | Differential Equations with Operator Coefficients |
| title_sort | differential equations with operator coefficients with applications to boundary value problems for partial differential equations |
| title_sub | with Applications to Boundary Value Problems for Partial Differential Equations |
| topic | Mathematics Differential Equations Ordinary Differential Equations Mathematik Operatorgleichung (DE-588)4043601-9 gnd Differentialoperator (DE-588)4012251-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Mathematics Differential Equations Ordinary Differential Equations Mathematik Operatorgleichung Differentialoperator Gewöhnliche Differentialgleichung |
| url | https://doi.org/10.1007/978-3-662-11555-8 |
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