Abstract We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the boundary value problem of an inhomogeneous partial differential equation with inhomogeneous, nonlocal boundary conditions. The construction applies for a broad class of linear partial differential equations and linear boundary conditions.

中文翻译：

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广义边值问题的格林函数解

摘要 我们从微分算子的基本解开始，构造满足非局部齐次边界条件的微分算子的格林函数表达式。这也为具有非齐次非局部边界条件的非齐次偏微分方程的边值问题提供了解决方案。该构造适用于广泛的线性偏微分方程和线性边界条件。