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On the Lyapunov Type Inequality

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Abstract

A.M. Lyapunov proved inequality, which enables us to estimate distance between two consecutive zeros a and b of the solution of linear differential equation of the second order x″(t) + q(t)x(t) = 0, where q(t) is a continuous for t ∈ [a, b] function. In the present paper we solve analogous problem for the linear differential equation x″(t) + p(t)x′(t) + q(t)x(t) = 0. The obtained inequality is applicable for estimations of the periods of periodic solutions of non-linear differential equations such as A. Lienard and B. Van der Pol equations.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, 74 R. Luxemburg str., Donetsk, 83114, Ukraine

    A. O. Ignatiev

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  1. A. O. Ignatiev
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Correspondence to A. O. Ignatiev.

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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 6, pp. 21–29.

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Ignatiev, A.O. On the Lyapunov Type Inequality. Russ Math. 64, 16–23 (2020). https://doi.org/10.3103/S1066369X20060043

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  • DOI: https://doi.org/10.3103/S1066369X20060043

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