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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 210325, 14 pages
http://dx.doi.org/10.1155/2012/210325
Research Article

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.

Linked References

  1. W. Li and Z. He, “The applications of theories of accretive operators to nonlinear elliptic boundary value problems in Lp-spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 46, no. 2, pp. 199–211, 2001. View at Publisher · View at Google Scholar
  2. L. Wei and H. Zhou, “The existence of solutions of nonlinear boundary value problems involving the P-Laplacian operator in Ls-spaces,” Journal of Systems Science and Complexity, vol. 18, no. 4, pp. 511–521, 2005.
  3. 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. View at Publisher · View at Google Scholar
  4. 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).
  5. 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).
  6. 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).
  7. 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. View at Publisher · View at Google Scholar
  8. 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. View at Publisher · View at Google Scholar
  9. B. D. Calvert and C. P. Gupta, “Nonlinear elliptic boundary value problems in Lp-spaces and sums of ranges of accretive operators,” Nonlinear Analysis, vol. 2, no. 1, pp. 1–26, 1978. View at Publisher · View at Google Scholar
  10. D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, ijthoff and Noordhoff International Publishers, Hague, The Netherlands, 1978.
  11. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste România, Bucharest, Romania, 1976.
  12. R. A. Adams, The Sobolev Space, People's Education Press, Beijing, China, 1981.
  13. 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. View at Publisher · View at Google Scholar
  14. E. Zeidler, Nonlinear Functional Analysis and its Applications (II), Springer-Verlag, New York, NY, USA, 1992.
  15. H. Brezis, “Integrales convexes dans les espaces de Sobolev,” Israel Journal of Mathematics, vol. 13, pp. 1–23, 1972.
  16. 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).
  17. W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, Japan, 2000.