Geodesic
Boundary value problem with an inner point for the singularly perturbed semilinear differential equations
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 1-8.

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In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $$ \epsilon y''+ky=f(t,y),\quad t\in \langle a,b \rangle , \ k0,\ 0\epsilon \ll 1 $$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.
DOI : 10.21136/MB.2011.141442
Classification : 34B10, 34B16, 34E05, 34E10, 34E20
Keywords: singular perturbation; boundary value problem; upper solution; lower solution 
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Vrábeľ, Róbert. Boundary value problem with an inner point for the singularly perturbed semilinear differential equations. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 1-8. doi : 10.21136/MB.2011.141442. http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141442/

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