In the paper, we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form Ax ∈ F(x), x ∈ U, where A:D(A)⊸E is an m-accretive operator in a Banach space E, F:K⊸E is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K ⊂ E. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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拟增殖算子的弱上半连续扰动的度数

在论文中，我们提供了一个重合度的构造，它是一个同伦不变量，用于检测方程或包含形式 Ax ∈ F(x), x ∈ U 的解的存在，其中 A:D(A)⊸E 是一个Banach 空间 E 中的 m-增积算子 F:K⊸E 是弱上半连续集值映射，约束到闭集 K ⊂ E 的开子集 U。提出了两种不同的方法。该理论被用于证明一些具有不连续性的非线性二阶偏微分方程的非平凡正解的存在性。本文是主题问题“微分方程和差分方程中的拓扑度和不动点理论”的一部分。