Solution of nonlinear elliptic boundary value problems and its iterative construction
type: Item
instance of: scholarly article
title: Solution of nonlinear elliptic boundary value problems and its iterative construction
zbMATH Open document ID: 1261.35064
DOI: 10.1155/2012/210325
author: Li Wei
author: Liling Duan
author: Haiyun Zhou
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We study a kind of nonlinear elliptic boundary value problems with generalized \(p\)-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.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 6134038
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/210325
OpenAlex ID: W2027969258
Wikidata QID: Q58695969
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description: scientific article; zbMATH DE number 6134038