In this note we formulate sufficient conditions under which a certain class of nonlinear and nonautonomous differential equations of second order is Hyers–Ulam stable. This class consists of equations obtained by perturbing Hill’s equation of the form \(x''=(\lambda ^2(t)-\lambda '(t))x\).

中文翻译：

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一类扰动希尔方程的Hyers-Ulam稳定性

在这篇笔记中，我们制定了充分条件，在该条件下，某类非线性和非自治二阶微分方程是 Hyers-Ulam 稳定的。该类由通过扰动\(x''=(\lambda ^2(t)-\lambda '(t))x\)形式的希尔方程获得的方程组成。