Oscillation Theory of Two-Term Differential Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1997
|
| Series: | Mathematics and Its Applications
396 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included |
| Physical Description: | 1 Online-Ressource (VII, 226 p) |
| ISBN: | 9789401725170 9789048148066 |
| DOI: | 10.1007/978-94-017-2517-0 |
Staff View
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| 500 | |a Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included | ||
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| indexdate | 2024-07-10T01:21:15Z |
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| isbn | 9789401725170 9789048148066 |
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| spelling | Elias, Uri Verfasser aut Oscillation Theory of Two-Term Differential Equations by Uri Elias Dordrecht Springer Netherlands 1997 1 Online-Ressource (VII, 226 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 396 Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included Mathematics Differential Equations Ordinary Differential Equations Mathematik Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s 1\p DE-604 https://doi.org/10.1007/978-94-017-2517-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Elias, Uri Oscillation Theory of Two-Term Differential Equations Mathematics Differential Equations Ordinary Differential Equations Mathematik 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 | Mathematics Differential Equations Ordinary Differential Equations Mathematik Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| topic_facet | Mathematics Differential Equations Ordinary Differential Equations Mathematik Lineare gewöhnliche Differentialgleichung |
| url | https://doi.org/10.1007/978-94-017-2517-0 |
| work_keys_str_mv | AT eliasuri oscillationtheoryoftwotermdifferentialequations |