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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 210325, 14 pages
Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction
1School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
2Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Shijiazhuang 050003, China
Received 4 September 2012; Accepted 15 October 2012
Academic Editor: Xiaolong Qin
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.
- W. Li and Z. He, “The applications of theories of accretive operators to nonlinear elliptic boundary value problems in -spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 46, no. 2, pp. 199–211, 2001.
- L. Wei and H. Zhou, “The existence of solutions of nonlinear boundary value problems involving the P-Laplacian operator in -spaces,” Journal of Systems Science and Complexity, vol. 18, no. 4, pp. 511–521, 2005.
- L. Wei and H. Zhou, “Research on the existence of solution of equation involving P-Laplacian operator,” Applied Mathematics a Journal of Chinese Universities B, vol. 21, no. 2, pp. 191–202, 2006.
- L. Wei and W. Y. Hou, “Study of the existence of the solution of nonlinear elliptic boundary value problems,” Journal of Hebei Normal University, vol. 28, no. 6, pp. 541–544, 2004 (Chinese).
- L. Wei and H. Y. Zhou, “Study of the existence of the solution of nonlinear elliptic boundary value problems,” Journal of Mathematical Research and Exposition, vol. 26, no. 2, pp. 334–340, 2006 (Chinese).
- L. Wei, “Existence of solutions of nonlinear boundary value problems involving the generalized P-Laplacian operator in a family of spaces,” Acta Analysis Functionalis Applicata, vol. 7, no. 4, pp. 354–359, 2005 (Chinese).
- L. Wei and R. P. Agarwal, “Existence of solutions to nonlinear Neumann boundary value problems with generalized P-Laplacian operator,” Computers & Mathematics with Applications, vol. 56, no. 2, pp. 530–541, 2008.
- L. Wei, H.-y. Zhou, and R. P. Agarwal, “Existence of solutions to nonlinear Neumann boundary value problems with P-Laplacian operator and iterative construction,” Acta Mathematicae Applicatae Sinica, vol. 27, no. 3, pp. 463–470, 2011.
- B. D. Calvert and C. P. Gupta, “Nonlinear elliptic boundary value problems in -spaces and sums of ranges of accretive operators,” Nonlinear Analysis, vol. 2, no. 1, pp. 1–26, 1978.
- D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, ijthoff and Noordhoff International Publishers, Hague, The Netherlands, 1978.
- V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste România, Bucharest, Romania, 1976.
- R. A. Adams, The Sobolev Space, People's Education Press, Beijing, China, 1981.
- S. Kamimura and W. Takahashi, “Strong convergence of a proximal-type algorithm in a Banach space,” SIAM Journal on Optimization, vol. 13, no. 3, pp. 938–945, 2002.
- E. Zeidler, Nonlinear Functional Analysis and its Applications (II), Springer-Verlag, New York, NY, USA, 1992.
- H. Brezis, “Integrales convexes dans les espaces de Sobolev,” Israel Journal of Mathematics, vol. 13, pp. 1–23, 1972.
- L. Wei and H. Y. Zhou, “An iterative convergence theorem of zero points for maximal monotone operators in Banach spaces and its application,” Mathematics in Practice and Theory, vol. 36, no. 5, pp. 235–242, 2006 (Chinese).
- W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, Japan, 2000.