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ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 7, pp. 885–897. c Pleiades Publishing, Ltd., 2007. Original Russian Text c G.V. Zavizion, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 7, pp. 867–878. ORDINARY DIFFERENTIAL EQUATIONS Singularly Perturbed System of Differential Equations with a Rational Singularity G. V. Zavizion Kirovograd State Pedagogical University, Kirovograd Received September 10, 2004 DOI: 10.1134/S0012266107070014 Asymptotic integration methods were developed for singularly perturbed systems of differential equations in [1–4] and other papers. Methods for finding asymptotic solutions were suggested in [5] for linear singularly perturbed systems of differential equations with an identically degenerate matrix multiplying the derivative. The methods in [1–5] cannot be used if the spectrum stability is violated inside the integration interval. Investigations of singularly perturbed linear systems of differential equations in the case of a turning point were carried out in [6–9]. The case of an unstable spectrum [4, p. 186] includes also the case in which the roots of the characteristic equation are discontinuous at isolated points of the integration interval. The structure of fundamental solutions of the second-order equations εxy + p(x)y + q(x)y =0,εx y + xp(x)y + q(x)y =0, where ε> 0 is a
Differential Equations – Springer Journals
Published: Oct 2, 2007
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