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Functional differential inequalities and estimation of the Cauchy function of an equation with aftereffect

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Abstract

We consider scalar functional differential inequalities that are used to estimate solutions to differential equations with deviating argument. A theorem on positiveness of the Cauchy function of a differential equation with aftereffect is derived from a theorem on a functional differential inequality with nonlinearmonotone operator, which is a direct generalization of the simplest classical theorem on a differential inequality. The suggested proofs rely on local properties of continuous functions only.

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Authors and Affiliations

  1. Perm National Research Polytechnic University, Komsomol’skii pr. 29, Perm, 614990, Russia

    K. M. Chudinov

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  1. K. M. Chudinov
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Correspondence to K. M. Chudinov.

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Dedicated to Professor N. V. Azbelev on the occasion of his 90th birthday

Original Russian Text © K.M. Chudinov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 4, pp. 52–61.

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Chudinov, K.M. Functional differential inequalities and estimation of the Cauchy function of an equation with aftereffect. Russ Math. 58, 44–51 (2014). https://doi.org/10.3103/S1066369X14040069

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