MATHEMATICA BOHEMICA, Vol. 136, No. 1, pp. 1-8, 2011

Boundary value problem with an inner point for the singularly perturbed semilinear
differential equations

Róbert Vrábeľ

Róbert Vrábeľ, Institute of Applied Informatics, Automation and Mathematics, Faculty of Materials Science and Technology, Hajdoczyho 1, 917 24 Trnava, Slovakia, e-mail: robert.vrabel@stuba.sk

Abstract: In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem
\epsilon y"+ky=f(t,y),\quad t\in\langle a,b \rangle, k<0, 0<\epsilon\ll1
satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.

Keywords: singular perturbation, boundary value problem, upper solution, lower solution

Classification (MSC 2010): 34B16

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