About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 182831, 19 pages
http://dx.doi.org/10.1155/2011/182831
Research Article

Existence Theory for Pseudo-Symmetric Solution to 𝑝 -Laplacian Differential Equations Involving Derivative

1School of Mathematics and Physics, XuZhou Institute of Technology, Xuzhou, Jiangsu 221008, China
2College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China

Received 19 November 2010; Accepted 2 May 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 You-Hui Su 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. C. Bai, “Triple positive solutions of three-point boundary value problems for fourth-order differential equations,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1364–1371, 2008. View at Publisher · View at Google Scholar
  2. R. Ma and H. Ma, “Positive solutions for nonlinear discrete periodic boundary value problems,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 136–141, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. Ma and B. Zhu, “Existence of positive solutions for a semipositone boundary value problem on the half-line,” Computers & Mathematics with Applications, vol. 58, no. 8, pp. 1672–1686, 2009. View at Publisher · View at Google Scholar
  4. J.-P. Sun and Y.-H. Zhao, “Multiplicity of positive solutions of a class of nonlinear fractional differential equations,” Computers & Mathematics with Applications, vol. 49, no. 1, pp. 73–80, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  5. D.-B. Wang and W. Guan, “Three positive solutions of boundary value problems for p-Laplacian difference equations,” Computers & Mathematics with Applications, vol. 55, no. 9, pp. 1943–1949, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Zhu and J. Zhu, “Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems,” Journal of Applied Mathematics and Computing, vol. 34, no. 1-2, pp. 393–405, 2010. View at Publisher · View at Google Scholar
  7. R. Avery and J. Henderson, “Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian,” Journal of Difference Equations and Applications, vol. 10, no. 6, pp. 529–539, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. I. Avery and J. Henderson, “Existence of three positive pseudo-symmetric solutions for a one-dimensional p-Laplacian,” Journal of Mathematical Analysis and Applications, vol. 277, no. 2, pp. 395–404, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Feng, X. Zhang, and W. Ge, “Exact number of pseudo-symmetric positive solutions for a p-Laplacian three-point boundary value problems and their applications,” Applied Mathematics and Computing, vol. 33, no. 1-2, pp. 437–448, 2010. View at Publisher · View at Google Scholar
  10. D. Ji, Y. Yang, and W. Ge, “Triple positive pseudo-symmetric solutions to a four-point boundary value problem with p-Laplacian,” Applied Mathematics Letters, vol. 21, no. 3, pp. 268–274, 2008. View at Publisher · View at Google Scholar
  11. D.-X. Ma and W.-G. Ge, “Existence and iteration of positive pseudo-symmetric solutions for a three-point second-order p-Laplacian BVP,” Applied Mathematics Letters, vol. 20, no. 12, pp. 1244–1249, 2007. View at Publisher · View at Google Scholar
  12. J. T. Cho and J.-I. Inoguchi, “Pseudo-symmetric contact 3-manifolds. II. When is the tangent sphere bundle over a surface pseudo-symmetric?” Note di Matematica, vol. 27, no. 1, pp. 119–129, 2007.
  13. S. W. Ng and A. D. Rae, “The pseudo symmetric structure of bis(dicyclohexylammonium) bis(oxalatotriphenylstannate),” Zeitschrift für Kristallographie, vol. 215, no. 3, pp. 199–204, 2000.
  14. T. Jankowski, “Existence of positive solutions to second order four-point impulsive differential problems with deviating arguments,” Computers & Mathematics with Applications, vol. 58, no. 4, pp. 805–817, 2009. View at Publisher · View at Google Scholar
  15. X.-F. Li and P.-H. Zhao, “The existence of triple positive solutions of nonlinear four-point boundary value problem with p–Laplacian,” Turkish Journal of Mathematics, vol. 33, no. 2, pp. 131–142, 2009.
  16. B. Sun and W. Ge, “Successive iteration and positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1772–1779, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Wang and W. Gao, “Existence of triple positive solutions for multi-point boundary value problems with a one dimensional p-Laplacian,” Computers & Mathematics with Applications, vol. 54, no. 6, pp. 793–807, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. F. Xu, L. Liu, and Y. Wu, “Multiple positive solutions of four-point nonlinear boundary value problems for a higher-order p-Laplacian operator with all derivatives,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 9, pp. 4309–4319, 2009. View at Publisher · View at Google Scholar
  19. R. I. Avery, “A generalization of the Leggett-Williams fixed point theorem,” Mathematical Sciences Research Hot-Line, vol. 3, no. 7, pp. 9–14, 1999.
  20. M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964.
  21. R. I. Avery and A. C. Peterson, “Three positive fixed points of nonlinear operators on ordered banach spaces,” Computers & Mathematics with Applications, vol. 42, no. 3-5, pp. 313–322, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1988.
  23. H. Wang, “Positive periodic solutions of functional differential equations,” Journal of Differential Equations, vol. 202, no. 2, pp. 354–366, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet