In this paper, we study sufficient conditions for the (strict) inverse-positivity of the linear fourth order operator corresponding to the one-dimensional beam equation with a spatially variable coefficient. We use a modification of results obtained by the operator reduction technique introduced by Schröder and show that the extrema of the coefficient can go beyond the originally derived bounds significantly.

中文翻译：

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扩展线性四阶算子的逆正性阈值

在本文中，我们研究了对应于具有空间可变系数的一维梁方程的线性四阶算子的（严格）逆正性的充分条件。我们使用由 Schröder 引入的算子缩减技术获得的结果的修改，并表明系数的极值可以显着超出最初导出的界限。