Abstract
We consider a system of first-order ordinary linear differential equations with coefficients depending on an arbitrary parameter λ. For large λ, if the coefficients are smooth with respect to x, then there are known classical exponentially asymptotic (with respect to λ) 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.
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Original Russian Text © A.I. Vagabov, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 16–22
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Vagabov, A.I. On the asymptotics with respect to a parameter of solutions of differential systems with coefficients in the class L q . Diff Equat 46, 17–23 (2010). https://doi.org/10.1134/S0012266110010039
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DOI: https://doi.org/10.1134/S0012266110010039