We prove a generalized Bôcher-type theorem for the nonhomogeneous Laplace’s equations on singular manifolds with conical metrics. More specifically, we give a sharp characterization of the behavior at isolated singularities of a solution bounded on one side for the equation \(\Delta _g u =f\) (\(f \in L_g^q\) with \(q > \frac{n}{2}\)). The main results in this paper imply that a nonnegative solution with conical singularities has certain of the attributes of fundamental solutions.

中文翻译：

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具有圆锥度量的流形上泊松方程的Bôcher型定理

我们证明了具有圆锥度量的奇异流形上非齐次Laplace方程的广义Bôcher型定理。更具体地说，对于方程\（\ Delta _g u = f \）（\（f \ in L_g ^ q \）带有\（q> \ frac {n} {2} \））。本文的主要结果表明，具有圆锥奇异性的非负解具有基本解的某些属性。