We study the existence of positive solutions for second-order nonlinear repulsive singular difference systems with periodic boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a fixed point theorem in cones and a nonlinear alternative principle of Leray-Schauder; the result is applicable to the case of a weak singularity as well as the case of a strong singularity. An example is given; some recent results in the literature are improved and generalized.

中文翻译：

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具有排斥奇异性的二阶非线性差分系统的多重正解

我们研究了具有周期性边界条件的二阶非线性排斥奇异差分系统的正解的存在性。我们的非线性在其因变量中可能是奇异的。主要结果的证明依赖于锥体中的不动点定理和 Leray-Schauder 的非线性替代原理；结果既适用于弱奇点的情况，也适用于强奇点的情况。给出了一个例子；最近文献中的一些结果得到了改进和概括。