Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/5676217 |
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| author | A. Gritsans F. Sadyrbaev I. Yermachenko |
| author_facet | A. Gritsans F. Sadyrbaev I. Yermachenko |
| author_sort | A. Gritsans |
| collection | DOAJ |
| description | We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory. |
| format | Article |
| id | doaj-art-3f69144aef5746fe981a3e4144867586 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-3f69144aef5746fe981a3e41448675862025-08-20T03:35:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/56762175676217Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear SystemA. Gritsans0F. Sadyrbaev1I. Yermachenko2Institute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaInstitute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaInstitute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaWe consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.http://dx.doi.org/10.1155/2016/5676217 |
| spellingShingle | A. Gritsans F. Sadyrbaev I. Yermachenko Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System International Journal of Differential Equations |
| title | Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System |
| title_full | Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System |
| title_fullStr | Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System |
| title_full_unstemmed | Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System |
| title_short | Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System |
| title_sort | dirichlet boundary value problem for the second order asymptotically linear system |
| url | http://dx.doi.org/10.1155/2016/5676217 |
| work_keys_str_mv | AT agritsans dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem AT fsadyrbaev dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem AT iyermachenko dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem |