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Asymptotics with respect to a parameter of solutions of linear functional-differential equations

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Abstract

We study the question of the number of linearly independent solutions of the equationy (n) (x)+(Fy) (x)+ρn y (x)=0,x∃ [0, 1], in which F is a bounded linear operator acting on various normed function spaces. A number of assertions about the asymptotic behavior of these solutions with respect to ρεℂ, tending to infinity are established.

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Authors and Affiliations

  1. Institute of Hydromechanics, Academy of Sciences of the Ukrainian SSR, Kiev

    A. M. Gomilko & G. V. Radzievskii

  2. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    A. M. Gomilko & G. V. Radzievskii

Authors
  1. A. M. Gomilko
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  2. G. V. Radzievskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1460–1469, November, 1990.

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Gomilko, A.M., Radzievskii, G.V. Asymptotics with respect to a parameter of solutions of linear functional-differential equations. Ukr Math J 42, 1301–1310 (1990). https://doi.org/10.1007/BF01066184

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  • DOI: https://doi.org/10.1007/BF01066184

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