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Uniform Estimates of Solutions of a Nonlinear Third-Order Differential Equation

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Abstract

One considers the differential equation

$$y{\prime\prime\prime}(x) + p\bigl(x, y(x), y{\prime}(x), y{\prime\prime}(x)\bigr) |y(x)|^{k-1} y(x) = 0,$$

where k > 1, the function p(x, y 0 , y 1 , y 2) is continuous and satisfies the inequalities

$$ 0 < p_* \le p(x, y_0, y_1, y_2) \le p^* < \infty,$$

as well as the Lipschitz condition with respect to the last three arguments. Uniform estimates are obtained for the moduli of the solutions with a common domain.

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Authors and Affiliations

  1. Moscow State University of Economics, Statistics, and Informatics, Moscow, Russia

    I. V. Astashova

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  1. I. V. Astashova
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Correspondence to I. V. Astashova.

Additional information

With deep gratitude to my teacher Prof. V. A. Kondratiev

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 29, Part I, pp. 146–161, 2013.

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Astashova, I.V. Uniform Estimates of Solutions of a Nonlinear Third-Order Differential Equation. J Math Sci 197, 237–247 (2014). https://doi.org/10.1007/s10958-014-1713-6

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