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An estimate for the spectral radius of an operator associated with an equation of neutral type

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Abstract

We obtain new bounds for the spectral radius of the operator (Ax) (t) = a(t)x(t−h) in spaces of functions which areω-periodic, almost periodic, and continuous and bounded on the whole axis. The results are used to prove a theorem on the existence ofω-periodic, bounded, and almost periodic solutions for linear functional-differential equations of neutral type.

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Literature cited

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Authors and Affiliations

  1. Voronezh State University, USSR

    É. Mukhamadiev & B. N. Sadovskii

Authors
  1. É. Mukhamadiev
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  2. B. N. Sadovskii
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 67–78, January, 1973.

The authors wish to thank M. A. Krasnosel'skii and V. Sh. Burd for discussion of this paper.

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Mukhamadiev, É., Sadovskii, B.N. An estimate for the spectral radius of an operator associated with an equation of neutral type. Mathematical Notes of the Academy of Sciences of the USSR 13, 39–45 (1973). https://doi.org/10.1007/BF01093627

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  • DOI: https://doi.org/10.1007/BF01093627

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