Abstract

Sufficient conditions for the existence of a generalized solution to a nonlinear elliptic differential equation with nonlocal boundary conditions of Bitsadze–Samarskii type are proved. The strong ellipticity condition is used for an auxiliary differential-difference operator. Under the formulated conditions, the differential-difference operator is demicontinuous, coercive, and has a semibounded variation, so the general theory of pseudomonotone operators can be applied.

中文翻译：

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论具有非局部边界条件的本质非线性椭圆微分方程的可解性

摘要

证明了具有 Bitsadze-Samarskii 型非局部边界条件的非线性椭圆微分方程广义解存在的充分条件。强椭圆性条件用于辅助微分-差分算子。在公式化的条件下，微分-差分算子是半连续的、强制的，并且具有半有界变分，因此可以应用伪单调算子的一般理论。