Non-linear boundary value problems with generalized p-Laplacian, ranges of m-accretive mappings and iterative schemes

Abstract

In this paper, we first prove some perturbation results on the ranges of maximal monotone operators, one of which is then used to show that the non-linear elltic equation involving the generalized -Laplacian operator with Neumann boundary conditions has a unique solution in . This unique solution is shown to be the zero point of a suitably defined non-linear m-accretive mapping. Finally, two kinds of iterative sequences are constructed and proved to converge strongly and weakly to the unique solution, respectively. Some new techniques of constructing appropriate operators and decomposing the equations are employed, which extend and complement some of the previous work.

Keywords:

• Monotone operator
• accretive mapping
• zero point
• generalized p-Laplacian operator
• non-linear elliptic boundary value problem
• iterative scheme.

AMS Subject Classifications:

• 47H05
• 47H09.

Acknowledgments

Supported by the National Natural Science Foundation of China (No. 11071053), the Natural Science Foundation of Hebei Province (No. A2010001482) and the Key Project of Science and Research of Hebei Education Department (No.ZH2012080).