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Entire Solutions of a Class of Nonlinear Algebraic Differential Equations

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Abstract

We study entire solutions (solutions that are entire functions) of algebraic differential equations of the form \(P(y,y^{(n)})+Q(z,y,y^{\prime },\ldots ,y^{(n)})=0 \) (where \(P \) and \(Q \) are polynomials with complex coefficients and the degree of \(Q \) is less than that of \(P \)). It is shown that (under certain constraints on the polynomial \(P \)) all entire transcendental solutions of such equations are quasipolynomials.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    A. Ya. Yanchenko

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  1. A. Ya. Yanchenko
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Correspondence to A. Ya. Yanchenko.

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Translated by V. Potapchouck

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Yanchenko, A.Y. Entire Solutions of a Class of Nonlinear Algebraic Differential Equations. Diff Equat 58, 1175–1181 (2022). https://doi.org/10.1134/S0012266122090026

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  • DOI: https://doi.org/10.1134/S0012266122090026

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