Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold
In this paper, we investigate the problem of existence and asymptotic behavior of the solutions for the nonlinear boundary value problem \begin{eqnarray*} \epsilon y''+ky=f(t,y),\quad t\in\langle a,b \rangle, \quad k>0,\quad 0<\epsilon<<1 \end{eqnarray*} satisfying Neumann boun...
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University of Szeged
2010-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=469 |
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doaj-4775982689834fe8b6fc0ec9d4c445262021-07-14T07:21:21ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752010-01-012010911110.14232/ejqtde.2010.1.9469Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifoldRobert Vrabel0Slovak Technical University Bratislava, Institute of Applied Informatics, Automation and Mathematics, Trnava, SlovakiaIn this paper, we investigate the problem of existence and asymptotic behavior of the solutions for the nonlinear boundary value problem \begin{eqnarray*} \epsilon y''+ky=f(t,y),\quad t\in\langle a,b \rangle, \quad k>0,\quad 0<\epsilon<<1 \end{eqnarray*} satisfying Neumann boundary conditions and where critical manifold is not normally hyperbolic. Our analysis relies on the method upper and lower solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=469 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Robert Vrabel |
| spellingShingle |
Robert Vrabel Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold Electronic Journal of Qualitative Theory of Differential Equations |
| author_facet |
Robert Vrabel |
| author_sort |
Robert Vrabel |
| title |
Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold |
| title_short |
Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold |
| title_full |
Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold |
| title_fullStr |
Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold |
| title_full_unstemmed |
Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold |
| title_sort |
singularly perturbed semilinear neumann problem with non-normally hyperbolic critical manifold |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
2010-01-01 |
| description |
In this paper, we investigate the problem of existence and asymptotic behavior of the solutions for the nonlinear boundary value problem
\begin{eqnarray*}
\epsilon y''+ky=f(t,y),\quad t\in\langle a,b \rangle, \quad k>0,\quad 0<\epsilon<<1
\end{eqnarray*}
satisfying Neumann boundary conditions and where critical manifold is not normally hyperbolic. Our analysis relies on the method upper and lower solutions. |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=469 |
| work_keys_str_mv |
AT robertvrabel singularlyperturbedsemilinearneumannproblemwithnonnormallyhyperboliccriticalmanifold |
| _version_ |
1721303813931925504 |