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Integral inequalities for Volterra's equation in a Banach space with a cone

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Abstract

A nonlinear Volterra equation with a continuous monotonic operator is investigated in a Banach space partially ordered by a cone. Existence of a solution is proved, and results are obtained concerning integral inequalities generalizing known strict and nonstrict inequalities.

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Authors and Affiliations

  1. Voronezh State University, USSR

    V. A. Bondarenko

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  1. V. A. Bondarenko
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Additional information

Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 151–160, February, 1971.

The author wishes to thank M. A. Krasnosel'skii and B. N. Sadovskii for their interest in this work.

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Bondarenko, V.A. Integral inequalities for Volterra's equation in a Banach space with a cone. Mathematical Notes of the Academy of Sciences of the USSR 9, 89–94 (1971). https://doi.org/10.1007/BF01316986

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  • DOI: https://doi.org/10.1007/BF01316986

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