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2012 Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction
Li Wei, Liling Duan, Haiyun Zhou
Abstr. Appl. Anal. 2012: 1-14 (2012). DOI: 10.1155/2012/210325


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.


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Li Wei. Liling Duan. Haiyun Zhou. "Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction." Abstr. Appl. Anal. 2012 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 28 March 2013

zbMATH: 1261.35064
MathSciNet: MR2999877
Digital Object Identifier: 10.1155/2012/210325

Rights: Copyright © 2012 Hindawi


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