Electron. J. Diff. Equ., Vol. 2011 (2011), No. 21, pp. 1-7.

A priori estimates for solutions to a four point boundary value problem for singularly perturbed semilinear differential equations

Robert Vrabel

This article concerns the existence and asymptotic behavior of solutions to a singularly perturbed second-order four-point boundary-value problem for nonlinear differential equations. Our analysis relies on the method of lower and upper solutions. We give accurate approximations of the solutions up to order $O(\epsilon)$.

Submitted January 5, 2010. Published February 7, 2011.
Math Subject Classifications: 34K10, 34K26.
Key Words: Singular perturbation; four point boundary value problem; lower and upper solutions.

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Robert Vrabel
Institute of Applied Informatics, Automation and Mathematics
Faculty of Materials Science and Technology
Hajdoczyho 1, 917 01 Trnava, Slovakia
email: robert.vrabel@stuba.sk, epsilon.phi1@gmail.com

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