In this paper, we investigate a class of p-Laplacian systems on a locally finite graph \(G=(V,E)\). By exploiting the method of Nehari manifold and some new analytical techniques, under suitable assumptions on the potentials and nonlinear terms, we prove that the p-Laplacian system admits a ground state solution \((u_{\lambda },v_{\lambda })\) when the parameter \(\lambda \) is sufficiently large. Furthermore, we consider the concentration behavior of these solutions as \(\lambda \rightarrow \infty \), and show that these solutions converge to a solution of the corresponding limit problem.

中文翻译：

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图上具有齐次非线性的 p-Laplacian 系统解的存在性和收敛性

在本文中，我们研究了局部有限图\(G=(V,E)\)上的一类p -拉普拉斯系统。通过利用 Nehari 流形的方法和一些新的分析技术，在对势和非线性项的适当假设下，我们证明了p -拉普拉斯系统允许基态解\((u_{\lambda },v_{\lambda } )\)当参数\(\lambda \)足够大时。此外，我们将这些解的集中行为视为\(\lambda \rightarrow \infty \)，并表明这些解收敛于相应极限问题的解。