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.
