Copyright © 2012 Li Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a kind of nonlinear elliptic boundary value problems with generalized -Laplacian operator. The unique solution is proved to be existing and the relationship between this solution and the zero point of a suitably defined nonlinear maximal monotone operator is investigated. Moreover, an iterative scheme is constructed to be strongly convergent to the unique solution. The work done in this paper is meaningful since it combines the knowledge of ranges for nonlinear operators, zero point of nonlinear operators, iterative schemes, and boundary value problems together. Some new techniques of constructing appropriate operators and decomposing the equations are employed, which extend and complement some of the previous work.