Existence of Three Solutions to a Class of Nonlinear Equations on Graphs  

作　　者：Yang LIU 

机构地区：[1]School of Mathematics,Renmin University of China,Beijing 100872,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第6期1129-1137,共9页数学学报（英文版）

摘　　要：Let be a function on locally finite connect graph G=(V,E)andΩbe a bounded subset of V.We consider the nonlinear Dirichlet boundary condition problem{-△u=f(u),inΩ,u=0,onδΩ.Let f:R→R be a function satisfying certain assumptions.Then under the functional framework we use the three-solution theorem and the variational method to prove that the above equation has at least three solutions,of which one is trivial and the others are strictly positive.

关 键 词：Multiple solutions three-solution theorem variational method locally finite graph 

分 类 号：O157.5[理学—数学]