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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