Title | The application of the comparison principle to the study of the properties of solutions of the Rayleigh differential equation |
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Authors | T. A. Gorshunova^{1}^{1}Moscow Polytechnic University |

Annotation | The set of the solutions of the equation of Rayleigh tending to zero in case of unlimited increase of independent variable is studied. Conditions under which the set of such decisions forms area in space of limited decisions are given. The problem about uniform boundedness and uniform asymptotic stability of solutions of the equation of Rayleigh is solved by method of comparing and a direct method of Lyapunov. |

Keywords | differential equations, equation of Rayleigh, the uniform asymptotic stability, the uniform limitation, Lyapunov's function, comparison method |

Citation | Gorshunova T. A. ''The application of the comparison principle to the study of the properties of solutions of the Rayleigh differential equation '' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 318-321. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper44.pdf. - Date of access: 24.08.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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