Abstract In this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

中文翻译：

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一般非局部条件变主系数三阶常微分方程格林泛函的构造

摘要 在这项工作中，研究了具有可变主系数的三阶线性常微分方程的一般非局部问题的可解性。一个新的伴随问题和格林泛函是为一个完全非齐次的问题构造的。提供了理论结果的几个说明性应用。