New criteria are established for the existence of positive solutions of a semipositone elliptic problem on the exterior of a ball in which the Neumann boundary conditions are non local. These criteria are determined by the relationship between the behaviour of the nonlinearity as the variable tends to 0 or $\infty$ and the principal (positive) eigenvalue of a suitable associate linear Hammerstein integral operator.

中文翻译：

---

外域半正Neumann椭圆问题的特征值准则

为球的外部存在一个半正椭圆问题的正解建立了新的准则，其中诺伊曼边界条件不是局部的。这些标准由非线性行为之间的关系确定，因为变量趋于0或$\infty$ 以及合适的准线性Hammerstein积分算子的主（正）特征值。