Existence and Convergence of Solutions for Nonlinear Elliptic Systems on Graphs  

作　　者：Jinyan Xu Liang Zhao 

机构地区：[1]School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems of MOE,Beijing Normal University,Beijing 100875,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第4期735-754,共20页数学与统计通讯（英文）

摘　　要：We consider a kind of nonlinear systems on a locally finite graph G=(V,E).We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solutionwhich depends on the parameterλwith some suitable assumptions on the potentials.Moreover,we pay attention to the concentration behavior of these solutions and prove that asλ→∞,these solutions converge to a ground state solution of a corresponding Dirichlet problem.Finally,we also provide some numerical experiments to illustrate our results.

关 键 词：Nonlinear elliptic system Locally finite graph Ground state solution 

分 类 号：O17[理学—数学]