Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator
含有广义p-Laplace算子的非线性边值问题解的存在性的研究

Two kinds of nonlinear boundary value problems with generalized p-Laplacian operator are studied in this paper. By using a result on the existence of solutions for variational inequalities, the result on the existence of solution of the nonlinear Dirichlet boundary value problem with generalized p-Laplacian operator is proved. Later, a kind of nonlinear Neumann boundary value problem with generalized p-Laplacian operator is presented. By digging deeply into the relationship between the above two kinds of nonlinear boundary value problems and by using a perturbation resulton the ranges of maximal monotone operators, an abstractresult for the existence of solution of the nonlinear Neumann boundary value problem with generalized p-Laplacianoperatoris obtained. In this paper, somenew prooftechniques areemployed, which extend and complement some of the previous research work.