Application of dynamical systems to the study of asymptotic properties of solutions to nonlinear higher-order differential equations.

*(English)*Zbl 1093.37005Summary: We study asymptotic properties of a higher-order, nonlinear, Emden-Fowler-type differential equation. We investigate asymptotics of all possible solutions of the equation in the cases of regular and singular nonlinearity for \(n = 3,4\). We use the method of change of variables, which allows one to reduce the initial equation of order \(n\) to a dynamical system on the (\(n - 1\))-dimensional compact sphere.

##### MSC:

37C10 | Dynamics induced by flows and semiflows |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

##### Keywords:

reduction; Emden-Fowler-type differential equation; asymptotics; method of change of variables
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\textit{I. V. Astashova}, J. Math. Sci., New York 126, No. 5, 1361--1391 (2005; Zbl 1093.37005)

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##### References:

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