Critical groups and multiple solutions of the image-Laplacian equations Original Research Article

In this paper, we give some results on the critical groups of the trivial solution u=0u=0 of the asymmetric p-Laplacian equation -▵pu=λ+|u|p-2u++λ-|u|p-2u--▵pu=λ+|u|p-2u++λ-|u|p-2u- Turn MathJax on with Dirichlet boundary value. Some applications to the existence of multiple solutions of the equation -▵pu=f(x,u)-▵pu=f(x,u) are given.