Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction. (18th November 2012)

• Record Type: Journal Article
• Authors: Wei, Li; Duan, Liling; Zhou, Haiyun
• Other Names: Qin Xiaolong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-11-18
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/210325
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study a kind of nonlinear elliptic boundary value problems with generalizedp -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.