AI 中文总结
本文推广Troesch方程以考虑电荷分离，得到两端具有边界层的显式近似解，并验证其精度，同时介绍一类超定一阶边值问题的相关结果。
AI 中文摘要
我们考虑Troesch经典两点边值问题的如下推广，以考虑物理要求所需的电荷分离：$w''=L\sinh(Lw), w(0)=W_0<0<W_1=w(1)$。与经典情形相反，该广义方程的解在两端均具有边界层。我们确定了一个显式近似解，并通过多种方式验证其精度。该解析解依赖于一类超定一阶边值问题的结果。阐述这一问题构成了本文的第二个目标。
英文摘要
We consider the following generalization of Troesch's classical two-point-BVP in order to take into account charge separation, which is required by physical considerations: $w''=L\sinh(Lw), w(0)=W_0<0<W_1=w(1)$. In contrast with the classical case, the solution of this generalized equation possesses boundary layer at both ends. We determine an explicit, approximate solution and verify its precision in several ways. The analytic solution hinges on a result concerning a class of overdetermined first order BVPs. Presenting this matter constitutes the second objective of the article.
