On asymptotic expansions of oscillating solutions of quasilinear ordinary differential equations systems

2013/06/28 by Kirill Vadimovich Amelkin, Amelkin, Kirill Vadimovich, Alexander Vasilevich Kostin +1
Engineering · Mathematics · #Differential Equations and Numerical Methods #Material Science and Thermodynamics #Numerical methods for differential equations #math.CA #msc:34C15 #msc:34E05

paper · pdf · doi:10.48550/arxiv.1306.6809

41 pages, in Russian, draft of 24.06.2013

arxiv created 2013/06/28 · arxiv updated 2013/07/01

Abstract

The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family of solutions) is investigated in two individual cases when all the eigenvalues of the matrix of the linear homogeneous part of the shorten system of differential equations 1) are not pure imaginary, 2) are simple and under some additional assumptions.

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