Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold

R. Vrabel, Institute of Applied Informatics, Automation and Mathematics, Trnava, Slovakia

E. J. Qualitative Theory of Diff. Equ., No. 9. (2010), pp. 1-11.

Abstract: 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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