The generalized Cauchy problem for singularly perturbed impulsive systems in the critical case

L. I. Karandzhulov, Ya. P. Stoyanova

Technical University of Sofia

Abstract: We construct an asymptotic expansion for solutions to nonlinear singularly perturbed systems of impulsive differential equations. We successively determine all terms of the asymptotic expansion by means of pseudoinverse matrices and orthoprojections.

Keywords: singular perturbation, asymptotic expansion, boundary function, pseudoinverse matrices, orthoprojections.

UDC: 517.925

Received: 16.12.2003
Revised: 14.11.2004

 English version: Siberian Mathematical Journal, 2006, 47:2, 269–290

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