In this paper, we investigate the generalized polynomial complementarity problem, which is a subclass of generalized complementarity problems with the involved map pairs being two polynomials. Based on the analysis on two structured tensor pairs located in the heading items of polynomials involved, and by using the degree theory, we achieve several results on the nonemptiness and compactness of solution sets. When generalized polynomial complementarity problems reduce to polynomial complementarity problems (or tensor complementarity problems), our results reduce to the existing ones. In particular, one of our results broadens the one proposed in a very recent paper to guarantee the nonemptiness and compactness of solution sets to generalized polynomial complementarity problems. Furthermore, we establish several existence and uniqueness results, which enrich the theory of generalized complementarity problems with the observation that some known conditions to guarantee the existence and uniqueness of solutions may not hold for a lot of generalized polynomial complementarity problems.

中文翻译：

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广义多项式互补问题解集的非空性和紧性

在本文中，我们研究了广义多项式互补问题，它是广义互补问题的一个子类，涉及的映射对是两个多项式。基于对位于所涉及多项式标题项中的两个结构化张量对的分析，利用度数理论，我们在解集的非空性和紧致性上得到了几个结果。当广义多项式互补问题归结为多项式互补问题（或张量互补问题）时，我们的结果归结为现有的问题。特别是，我们的一个结果扩展了最近一篇论文中提出的结果，以保证广义多项式互补问题的解集的非空性和紧凑性。此外，我们建立了几个存在性和唯一性结果，