拟线性常微分方程组振动解的渐近展开
On asymptotic expansions of oscillating solutions of quasilinear ordinary differential equations systems
摘要：
证明了拟线性常微分方程系统在一定条件下存在振动型形式特解（解族）。本文在两种情况下研究了该解（解族）的渐近性质，即当缩短的微分方程组的线性齐次部分的矩阵的特征值1）不是纯虚的，2）是简单的，并在某些附加的假设下.
英文摘要：
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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