Abstract

A second-order differential equation with periodic coefficients is considered. The reduction of this equation to a first-order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu equation describing the behavior of solutions near the boundaries of these zones.

中文翻译：

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第二和第三共振区边界附近的马修方程

摘要

考虑具有周期系数的二阶微分方程。显示了将该方程简化为一阶非线性方程。为描述这些区域边界附近解的行为的 Mathieu 方程构造了第二共振区的第四次近似和第三共振区的第三次近似。