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Structure of formal solutions of singularly perturbed n-th-order differential equations

Authors:	G S Zhukova N P Chernykh

Institution:	(1) Voronezh University, USSR

Abstract:	Conclusions If the defining equation corresponding to the number k₀<0 has a multiple root ₀(t) $(i.e., \frac{{dL}}{{d\mu _0 }}(t) \equiv 0\forall t \in 0, T])$ , then Theorem I is inapplicable. In this case to find particular solutions of (I) one should, with the help of the substitution (t)=^k ₀₀(t)+(t) pass to an equation for (t) and investigate it by the method of Newton's diagram.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 6, pp. 695–702, November–December, 1985.

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