Three point boundary value problem for singularly perturbed semilinear differential equations.

Vrábel, Róbert

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Nonlocal four-point boundary value problem for the singularly perturbed semilinear differential equations.

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

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In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $ϵ y^{''} + k y = f (t, y), t \in 〈 a, b 〉, k < 0, 0 < ϵ ≪ 1$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.