Three point boundary value problem for singularly perturbed semilinear differential equations

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

E. J. Qualitative Theory of Diff. Equ., No. 70. (2009), pp. 1-4.

Abstract: In this paper, we investigate the problem of existence and asymptotic behavior of 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 three point boundary conditions. Our analysis relies on the method of lower and upper solutions.

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