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This paper deals with the three-point boundary value problem for the nonlinear singularly perturbed second-order systems. Especially, we focus on an analysis of the solutions in the right endpoint of considered interval from an appearance of the boundary layer point of view. We use the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear systems considered here.

Boundary Value Problem for Nonlinear Singularity perturbed Systems in Critical case of Exchange of Stability

L. I. Karandjulov, Y. P. Stoyanova (2003)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

Karandjulov, L., Stoyanova, Y. (2000)

Serdica Mathematical Journal

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Calcul des couches limites dans une membrane porteuse de charges électriques fixes

Jean-Pierre Kernévez, Alain Trubuil (1986)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Canards et enlacements

E. Benoît (1990)

Publications Mathématiques de l'IHÉS

Champs lents-rapides complexes à une dimension lente

Jean-Louis Callot (1993)

Annales scientifiques de l'École Normale Supérieure

Clustering layers and boundary layers in spatially inhomogeneous phase transition problems

Kimie Nakashima, Kazunaga Tanaka (2003)

Annales de l'I.H.P. Analyse non linéaire

Connecting fast-slow systems and Conley index theory via transversality.

Kuehn, Christian (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case.

Slavova, Angela (1993)

Journal of Applied Mathematics and Stochastic Analysis

Convergence estimate for second order Cauchy problems with a small parameter

Branko Najman (1998)

Czechoslovak Mathematical Journal

We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $ε .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.

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Applications of the method of barriers. II: Some singularly perturbed problems.

Asymptotic behavior of $T$ -periodic solutions of singularly perturbed second-order differential equation

Asymptotic numerical method for singularly perturbed third order ordinary differential equations with a discontinuous source term.

Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay

Averaging of multivalued differential equations.

Bifurcation of an invariant torus of a system of differential equations in the degenerate case.

Boundary layer phenomena for differential-delay equations with state dependent time lags: II.

Boundary layer phenomenon for three -point boundary value problem for the nonlinear singularly perturbed systems