# zbMATH — the first resource for mathematics

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
Full Text: