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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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1417-3875 1417-3875 |