This article is cited in 5 papers

On the asymptotics with respect to a parameter of solutions of differential systems with coefficients in the class $L_q$

A. I. Vagabov

Daghestan State University, Makhachkala

Abstract: We consider a system of first-order ordinary linear differential equations with coefficients depending on an arbitrary parameter $\lambda$. For large $\lambda$, if the coefficients are smooth with respect to $x$, then there are known classical exponentially asymptotic (with respect to $\lambda$) formulas for the solution of the system. We generalize such formulas to the case in which the coefficients belong to the class $L_q$, $q>1$. We use a new method for the reduction of problems to an integral system of special form.

UDC: 517.928

Received: 25.03.2009

 English version: Differential Equations, 2010, 46:1, 17–23

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