Green's functions to linear second-order ordinary differential equations with general separated boundary conditions (BCs) are derived, where the parameters used in the BCs are allowed to take negative values. Previous results only considered the nonnegative parameters and such separated BCs arise in the usual Thomas–Fermi BCs. Properties of the Green's functions with possibly negative parameters are obtained and are new. As applications, we study the steady-state solutions of the one-dimensional diffusion advection models arising in chemical reactor theory and mathematical biology. We exhibit that the BCs arising from the one- dimensional diffusion advection models contain negative parameters.

中文翻译：

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格林函数、线性二阶微分方程和一维扩散对流模型

导出了具有一般分离边界条件 (BC) 的线性二阶常微分方程的格林函数，其中允许在 BC 中使用的参数取负值。以前的结果只考虑了非负参数，并且这种分离的 BC 出现在通常的 Thomas-Fermi BC 中。获得可能为负参数的格林函数的属性并且是新的。作为应用，我们研究了化学反应器理论和数学生物学中出现的一维扩散平流模型的稳态解。我们展示了由一维扩散平流模型产生的 BC 包含负参数。