摘要
Let G = （V,E） be a locally finite graph, Ω C V be a finite connected set, A be the graph Laplacian, and suppose that h ： V →R is a function satisfying the coercive condition on Ω, namely there exists some constant δ〉 0 such that Ωu（-△＋h）udμ≥δ Ω｜u｜^2dμ, u：VR. By the mountain-pass theorem of Ambrosette-Rabinowitz, we prove that for any p 〉 2, there exists a positive solution to -△μ＋hu=｜u｜^p-2u in Ω. Using the same method, we prove similar results for the p-Laplacian equations. This partly improves recent results of Grigor＇yan-Lin-Yang.
