Semi-linear Elliptic Equations on Graph  

作　　者：ZHANG Dongshuang 

机构地区：[1]Department of Mathematics, Renmin University of China, Beijing 100872, China

出　　处：《Journal of Partial Differential Equations》2017年第3期221-231,共11页偏微分方程（英文版）

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.

关 键 词：SOBOLEV EMBEDDING Yamabe type equation LAPLACIAN on graph. 

分 类 号：O175.27[理学—数学]