The Nonlinear Limit-Point/Limit-Circle Problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | First posed by Hermann Weyl in 1910, the limit–point/limit–circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations. This self-contained monograph traces the evolution of this problem from its inception to its modern-day extensions to the study of deficiency indices and analogous properties for nonlinear equations. The book opens with a discussion of the problem in the linear case, as Weyl originally stated it, and then proceeds to a generalization for nonlinear higher-order equations. En route, the authors distill the classical theorems for second and higher-order linear equations, and carefully map the progression to nonlinear limit–point results. The relationship between the limit–point/limit–circle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limit–point/limit–circle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields |
| Beschreibung: | 1 Online-Ressource (IX, 162 p) |
| ISBN: | 9780817682187 9780817635626 |
| DOI: | 10.1007/978-0-8176-8218-7 |
Internformat
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Datensatz im Suchindex
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| author | Bartušek, Miroslav |
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| format | Electronic eBook |
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| spelling | Bartušek, Miroslav Verfasser aut The Nonlinear Limit-Point/Limit-Circle Problem by Miroslav Bartušek, Zuzana Došlá, John R. Graef Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (IX, 162 p) txt rdacontent c rdamedia cr rdacarrier First posed by Hermann Weyl in 1910, the limit–point/limit–circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations. This self-contained monograph traces the evolution of this problem from its inception to its modern-day extensions to the study of deficiency indices and analogous properties for nonlinear equations. The book opens with a discussion of the problem in the linear case, as Weyl originally stated it, and then proceeds to a generalization for nonlinear higher-order equations. En route, the authors distill the classical theorems for second and higher-order linear equations, and carefully map the progression to nonlinear limit–point results. The relationship between the limit–point/limit–circle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limit–point/limit–circle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields Mathematics Global analysis (Mathematics) Functional equations Functional analysis Differential Equations Ordinary Differential Equations Analysis Difference and Functional Equations Functional Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s 1\p DE-604 Došlá, Zuzana Sonstige oth Graef, John R. Sonstige oth https://doi.org/10.1007/978-0-8176-8218-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bartušek, Miroslav The Nonlinear Limit-Point/Limit-Circle Problem Mathematics Global analysis (Mathematics) Functional equations Functional analysis Differential Equations Ordinary Differential Equations Analysis Difference and Functional Equations Functional Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4134367-0 |
| title | The Nonlinear Limit-Point/Limit-Circle Problem |
| title_auth | The Nonlinear Limit-Point/Limit-Circle Problem |
| title_exact_search | The Nonlinear Limit-Point/Limit-Circle Problem |
| title_full | The Nonlinear Limit-Point/Limit-Circle Problem by Miroslav Bartušek, Zuzana Došlá, John R. Graef |
| title_fullStr | The Nonlinear Limit-Point/Limit-Circle Problem by Miroslav Bartušek, Zuzana Došlá, John R. Graef |
| title_full_unstemmed | The Nonlinear Limit-Point/Limit-Circle Problem by Miroslav Bartušek, Zuzana Došlá, John R. Graef |
| title_short | The Nonlinear Limit-Point/Limit-Circle Problem |
| title_sort | the nonlinear limit point limit circle problem |
| topic | Mathematics Global analysis (Mathematics) Functional equations Functional analysis Differential Equations Ordinary Differential Equations Analysis Difference and Functional Equations Functional Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Functional equations Functional analysis Differential Equations Ordinary Differential Equations Analysis Difference and Functional Equations Functional Analysis Mathematik Nichtlineare Differentialgleichung Asymptotisches Lösungsverhalten |
| url | https://doi.org/10.1007/978-0-8176-8218-7 |
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