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Second solutions of equations involving positive operators in degenerate cases

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Abstract

A theorem, is proved concerning the existence of nonzero fixed points of a positive completely continuous operator, linearly degenerate at zero and infinity.

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Literature cited

  1. M. A. Krasnosel'skii, Positive Solutions of Operational Equations [in Russian], Moscow (1962).

  2. M. A. Krasnosel'skii, “Fixed points of operators which contract or expand a cone,” Dokl. Akad. Nauk SSSR, 135, No. 3, 527–530 (1960).

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  3. Yu. V. Pokornii, “Operators contracting or expanding a cone,” Dokl. Akad.UkrSSR,6, 705–709 (1963).

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  4. M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Moscow (1956).

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Authors and Affiliations

  1. Voronezh State University, USSR

    I. N. Astaf'eva & V. I. Malovikov

Authors
  1. I. N. Astaf'eva
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  2. V. I. Malovikov
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Additional information

Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 143–149, February, 1971.

The authors wish to thank Yu. V. Pokornii for directing this work.

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Astaf'eva, I.N., Malovikov, V.I. Second solutions of equations involving positive operators in degenerate cases. Mathematical Notes of the Academy of Sciences of the USSR 9, 85–88 (1971). https://doi.org/10.1007/BF01316985

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  • DOI: https://doi.org/10.1007/BF01316985

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