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Application of dynamical systems to the study of asymptotic properties of solutions to nonlinear higher-order differential equations. (English) Zbl 1093.37005
Summary: 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
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