Abstract

We establish estimates (interior and up to the boundary) of solutions of the inequality \(\mathscr {L}(u)\geq 0\), where \(\mathscr {L} \) is a linear second-order differential operator with impulse singularities. The results in particular apply to the Neumann boundary value problem. The relationship between this inequality and the class of concave functions of one variable is studied.

中文翻译：

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具有脉冲奇异性的微分不等式解的估计

摘要

我们建立不等式\（\ mathscr {L}（u）\ geq 0 \）的解的估计（内部和边界） ，其中\（\ mathscr {L} \）是线性二阶微分算子具有冲动奇点。该结果尤其适用于诺伊曼边值问题。研究了该不等式与一个变量的凹函数类别之间的关系。