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Approximate computation of the positive eigenvalue of a positive operator with a nonlinear occurrence of a parameter

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Abstract

A method is indicated for the approximate determination of the positive eigenvalue of the problem x−Qλx=0, λ>0, xεK, x≠0, whereK is a cone in Banach space and Qλ is an operator-valued function positive relative toK.

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Literature cited

  1. B. A. Ivanov, “On the properties of eigenvalues of positive operators depending non-linearly on a parameter,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Akad. Nauk SSSR,56, 177–181 (1975).

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  2. I. Marek, “Generalization of the minimax principle for indecomposable operators,” Dokl. Akad. Nauk SSSR,176, 780–782 (1967).

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  3. I. Marek, “Spectral radius of indecomposable positive operators,” Dokl. Akad. Nauk SSSR,176, 1009–1011 (1967).

    Google Scholar 

  4. M. G. Krein and M. A. Rutman, “Linear operators leaving a cone in Banach space invariant,” Usp. Mat. Nauk,3, No. 1, 3–95 (1948).

    Google Scholar 

  5. V. Z. Belen'kii, V. A. Volkonskii, and N. V. Pavlov, “Dynamic input-output models,” Ekonomika Mat. Metody,8, No. 4, 493–511 (1972).

    Google Scholar 

  6. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).

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Authors
  1. B. A. Ivanov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 37–39, 1976.

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Ivanov, B.A. Approximate computation of the positive eigenvalue of a positive operator with a nonlinear occurrence of a parameter. J Math Sci 13, 216–217 (1980). https://doi.org/10.1007/BF01296235

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  • DOI: https://doi.org/10.1007/BF01296235

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