Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2009 (2009), Article ID 512402, 21 pages
http://dx.doi.org/10.1155/2009/512402
Research Article

Existence of Positive Solutions to Singular 𝑝 -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

1College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China
2School of Mathematics and Physics, XuZhou Institute of Technology, Xuzhou, Jiangsu 221008, China
3Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China

Received 27 December 2008; Revised 21 February 2009; Accepted 25 February 2009

Academic Editor: Paul Eloe

Copyright © 2009 Qiying 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. S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, Germany, 1988.
  2. R. P. Agarwal, M. Bohner, and P. Řehák, “Half-linear dynamic equations,” in Nonlinear Analysis and Applications: to V. Lakshmikantham on His 80th Birthday. Vol. 1, pp. 1–57, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001. View at Zentralblatt MATH · View at MathSciNet
  4. M. A. Jones, B. Song, and D. M. Thomas, “Controlling wound healing through debridement,” Mathematical and Computer Modelling, vol. 40, no. 9-10, pp. 1057–1064, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. V. Spedding, “Taming nature's numbers,” New Scientist, no. 2404, pp. 28–32, July 2003. View at Google Scholar
  6. D. M. Thomas, L. Vandemuelebroeke, and K. Yamaguchi, “A mathematical evolution model for phytoremediation of metals,” Discrete and Continuous Dynamical Systems. Series B, vol. 5, no. 2, pp. 411–422, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  8. B. Aulbach and L. Neidhart, “Integration on measure chains,” in Proceedings of 6th International Conference on Difference Equations, pp. 239–252, CRC, Augsburg, Germany, July-August 2004. View at Zentralblatt MATH · View at MathSciNet
  9. C. J. Chyan and P. J. Y. Wong, “Multiple positive solutions of conjugate boundary value problems on time scales,” Taiwanese Journal of Mathematics, vol. 11, no. 2, pp. 421–445, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Hoffacker, “Green's functions and eigenvalue comparisons for a focal problem on time scales,” Computers & Mathematics with Applications, vol. 45, no. 6–9, pp. 1339–1368, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Hoffacker and C. C. Tisdell, “Stability and instability for dynamic equations on time scales,” Computers & Mathematics with Applications, vol. 49, no. 9-10, pp. 1327–1334, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. D. R. Anderson, G. Sh. Guseinov, and J. Hoffacker, “Higher-order self-adjoint boundary-value problems on time scales,” Journal of Computational and Applied Mathematics, vol. 194, no. 2, pp. 309–342, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. W.-T. Li and X.-L. Liu, “Eigenvalue problems for second-order nonlinear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 318, no. 2, pp. 578–592, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y.-H. Su and W.-T. Li, “Triple positive symmetric solutions of p-Laplacian BVPs on time scales,” Acta Mathematica Sinica, Chinese Series, vol. 52, pp. 181–196, 2009. View at Google Scholar
  15. Y.-H. Su, X. H. Yuan, and X.-X. Yan, “Existence of solution to a three-point BVPs for p-Laplacian dynamic equations on time scales,” Journal of Lanzhou University, Natural Sciences, vol. 44, pp. 112–116, 2008. View at Google Scholar
  16. J.-P. Sun, “Existence of solution and positive solution of BVP for nonlinear third-order dynamic equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 3, pp. 629–636, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Anderson, R. Avery, and J. Henderson, “Existence of solutions for a one dimensional p-Laplacian on time-scales,” Journal of Difference Equations and Applications, vol. 10, no. 10, pp. 889–896, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. He, “Double positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales,” Journal of Computational and Applied Mathematics, vol. 182, no. 2, pp. 304–315, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y.-H. Su, “Multiple positive pseudo-symmetric solutions of p-Laplacian dynamic equations on time scales,” Mathematical and Computer Modelling, vol. 49, no. 7-8, pp. 1664–1681, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Y.-H. Su and W.-T. Li, “Triple positive solutions of m-point BVPs for p-Laplacian dynamic equations on time scales,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 3811–3820, 2008. View at Google Scholar · View at MathSciNet
  21. Y.-H. Su, W.-T. Li, and H.-R. Sun, “Triple positive pseudo-symmetric solutions of three-point BVPs for p-Laplacian dynamic equations on time scales,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 6, pp. 1442–1452, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. H.-R. Sun and W.-T. Li, “Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales,” Journal of Differential Equations, vol. 240, no. 2, pp. 217–248, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Y.-H. Su and W.-T. Li, “Existence of positive solutions to a singular p-Laplacian dynamic equations with sign changing nonlinearity,” Acta Mathematica Sinica, Chinese Series, vol. 28, pp. 51–60, 2008. View at Google Scholar
  24. Y.-H. Su, W.-T. Li, and H.-R. Sun, “Positive solutions of singular p-Laplacian dynamic equations with sign changing nonlinearity,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 352–368, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Y.-H. Su, W.-T. Li, and H.-R. Sun, “Positive solutions of singular p-Laplacian BVPs with sign changing nonlinearity on time scales,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 845–858, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. R. P. Agarwal, H. Lü, and D. O'Regan, “Existence theorems for the one-dimensional singular p-Laplacian equation with sign changing nonlinearities,” Applied Mathematics and Computation, vol. 143, no. 1, pp. 15–38, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D. O'Regan, “Upper and lower solutions for singular problems arising in the theory of membrane response of a spherical cap,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 2, pp. 1163–1174, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. H. Lü, D. O'Regan, and R. P. Agarwal, “Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition,” Journal of Computational and Applied Mathematics, vol. 182, no. 1, pp. 188–210, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. H. Lü, D. O'Regan, and R. P. Agarwal, “Upper and lower solutions for the singular p-Laplacian with sign changing nonlinearities and nonlinear boundary data,” Journal of Computational and Applied Mathematics, vol. 181, no. 2, pp. 442–466, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. D. Q. Jiang, D. O'Regan, and R. P. Agarwal, “A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian,” Journal of Applied Analysis, vol. 11, no. 1, pp. 35–47, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. V. Lakshmikantham, S. Sivasundaram, and B. Kaymakcalan, Dynamic Systems on Measure Chains, vol. 370 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. View at Zentralblatt MATH · View at MathSciNet