Using monotonicity methods, the Lagrange multiplier rule, and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper.

中文翻译：

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涉及单调算子的非线性方程的定位特性

使用单调性方法，拉格朗日乘数规则和一些变分参数，我们考虑了一种局部化结果，该结果与闭合球上动作功能的临界点的存在有关。获得希尔伯特和巴纳赫空间中球上的Schechter临界点定理的变体。最后一部分给出了非线性Dirichlet问题和偏差分方程的应用。