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

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Abstract

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.

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Authors
  1. I. V. Astashova
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 8 , Suzdal Conference—2, 2003.

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Astashova, I.V. Application of dynamical systems to the study of asymptotic properties of solutions to nonlinear higher-order differential equations. J Math Sci 126, 1361–1391 (2005). https://doi.org/10.1007/PL00021970

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