Nonlinear Singular Perturbation Phenomena: Theory and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1984
|
| Schriftenreihe: | Applied Mathematical Sciences
56 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the existence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly questions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary differential equations, by means of the consistent use of differential inequality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equations. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council |
| Beschreibung: | 1 Online-Ressource (VIII, 180p. 12 illus) |
| ISBN: | 9781461211143 9780387960661 |
| DOI: | 10.1007/978-1-4612-1114-3 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Chang, K. W. |
| author_facet | Chang, K. W. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1114-3 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211143 9780387960661 |
| language | English |
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| physical | 1 Online-Ressource (VIII, 180p. 12 illus) |
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| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Chang, K. W. Verfasser aut Nonlinear Singular Perturbation Phenomena Theory and Applications by K. W. Chang, F. A. Howes New York, NY Springer New York 1984 1 Online-Ressource (VIII, 180p. 12 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 56 Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the existence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly questions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary differential equations, by means of the consistent use of differential inequality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equations. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council Mathematics Global analysis (Mathematics) Analysis Mathematik Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Nichtlineare singuläre Störung (DE-588)4171759-4 gnd rswk-swf Nichtlineares Randwertproblem (DE-588)4129830-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Singuläre Störung (DE-588)4055100-3 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Nichtlineares Randwertproblem (DE-588)4129830-5 s 2\p DE-604 Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 s 3\p DE-604 Nichtlineare singuläre Störung (DE-588)4171759-4 s 4\p DE-604 Howes, F. A. Sonstige oth Applied Mathematical Sciences 56 (DE-604)BV040244599 56 https://doi.org/10.1007/978-1-4612-1114-3 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chang, K. W. Nonlinear Singular Perturbation Phenomena Theory and Applications Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Analysis Mathematik Singuläre Störung (DE-588)4055100-3 gnd Nichtlineare singuläre Störung (DE-588)4171759-4 gnd Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd |
| subject_GND | (DE-588)4055100-3 (DE-588)4171759-4 (DE-588)4129830-5 (DE-588)4128130-5 (DE-588)4048395-2 (DE-588)4478411-9 |
| title | Nonlinear Singular Perturbation Phenomena Theory and Applications |
| title_auth | Nonlinear Singular Perturbation Phenomena Theory and Applications |
| title_exact_search | Nonlinear Singular Perturbation Phenomena Theory and Applications |
| title_full | Nonlinear Singular Perturbation Phenomena Theory and Applications by K. W. Chang, F. A. Howes |
| title_fullStr | Nonlinear Singular Perturbation Phenomena Theory and Applications by K. W. Chang, F. A. Howes |
| title_full_unstemmed | Nonlinear Singular Perturbation Phenomena Theory and Applications by K. W. Chang, F. A. Howes |
| title_short | Nonlinear Singular Perturbation Phenomena |
| title_sort | nonlinear singular perturbation phenomena theory and applications |
| title_sub | Theory and Applications |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Singuläre Störung (DE-588)4055100-3 gnd Nichtlineare singuläre Störung (DE-588)4171759-4 gnd Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Singuläre Störung Nichtlineare singuläre Störung Nichtlineares Randwertproblem Numerisches Verfahren Randwertproblem Nichtlineare gewöhnliche Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-1114-3 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT changkw nonlinearsingularperturbationphenomenatheoryandapplications AT howesfa nonlinearsingularperturbationphenomenatheoryandapplications |