Resonant Problems by Quasilinearization
The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem ha...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2014/564914 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849683480470880256 |
|---|---|
| author | Nadezhda Sveikate |
| author_facet | Nadezhda Sveikate |
| author_sort | Nadezhda Sveikate |
| collection | DOAJ |
| description | The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples. |
| format | Article |
| id | doaj-art-d8384d1781a34c26aba9e918abd8315f |
| institution | DOAJ |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-d8384d1781a34c26aba9e918abd8315f2025-08-20T03:23:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512014-01-01201410.1155/2014/564914564914Resonant Problems by QuasilinearizationNadezhda Sveikate0Faculty of Natural Sciences and Mathematics, Daugavpils University, Parādes Street 1, Daugavpils 5401, LatviaThe Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples.http://dx.doi.org/10.1155/2014/564914 |
| spellingShingle | Nadezhda Sveikate Resonant Problems by Quasilinearization International Journal of Differential Equations |
| title | Resonant Problems by Quasilinearization |
| title_full | Resonant Problems by Quasilinearization |
| title_fullStr | Resonant Problems by Quasilinearization |
| title_full_unstemmed | Resonant Problems by Quasilinearization |
| title_short | Resonant Problems by Quasilinearization |
| title_sort | resonant problems by quasilinearization |
| url | http://dx.doi.org/10.1155/2014/564914 |
| work_keys_str_mv | AT nadezhdasveikate resonantproblemsbyquasilinearization |