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Asymptotics of the system of solutions of a general differential equation with parameter

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Abstract

We consider annth-order differential equation

$$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$

with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that\(j = \overline {1,n} \) anda 0 (x) is an absolutely continuous function which does not turn into zero on the interval [a, b], we establish asymptotic formulas of exponential type for the fundamental system of solutions of this equation provided that |λ| is sufficiently large.

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Authors
  1. V. S. Rykhlov
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Rykhlov, V.S. Asymptotics of the system of solutions of a general differential equation with parameter. Ukr Math J 48, 108–121 (1996). https://doi.org/10.1007/BF02390988

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  • DOI: https://doi.org/10.1007/BF02390988

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