About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 506716, 15 pages
http://dx.doi.org/10.1155/2012/506716
Research Article

Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

Department of Mathematics, Ege University, Izmir, 35100 Bornova, Turkey

Received 2 August 2012; Accepted 8 November 2012

Academic Editor: Yongfu Su

Copyright © 2012 Fatma Tokmak and Ilkay Yaslan Karaca. 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, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990. View at Zentralblatt MATH
  2. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, 2001. View at Publisher · View at Google Scholar
  3. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, 2003.
  4. J. Adem and M. Moshinsky, “Self-adjointness of a certain type of vectorial boundary value problems,” Boletín de la Sociedad Matemática Mexicana, vol. 7, pp. 1–17, 1950.
  5. V. A. Ilin and E. I. Moiseev, “Nonlocal boundary value problem of the second kind for a Sturm-CLiouville operator,” Difference Equation, vol. 23, pp. 979–987, 1987.
  6. Z. Bai, W. Ge, and Y. Wang, “Multiplicity results for some second-order four-point boundary-value problems,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 60, no. 3, pp. 491–500, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Zou, Q. Hu, and R. Zhang, “On numerical studies of multi-point boundary value problem and its fold bifurcation,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 527–537, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. R. Avery, J. Henderson, and D. O'Regan, “Four functionals fixed point theorem,” Mathematical and Computer Modelling, vol. 48, no. 7-8, pp. 1081–1089, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Z. Bai and W. Ge, “Existence of three positive solutions for some second-order boundary value problems,” Computers & Mathematics with Applications, vol. 48, no. 5-6, pp. 699–707, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. T.-T. Sun, L.-L. Wang, and Y.-H. Fan, “Existence of positive solutions to a nonlocal boundary value problem with p-Laplacian on time scales,” Advances in Difference Equations, Article ID 809497, 15 pages, 2010.
  12. J. Liu and H.-R. Sun, “Multiple positive solutions for m-point boundary value problem on time scales,” Boundary Value Problems, vol. 2011, Article ID 591219, 2011.
  13. F. Xu and Z. Meng, “The existence of positive solutions for third-order p-Laplacian m-point boundary value problems with sign changing nonlinearity on time scales,” Advances in Difference Equations, vol. 2009, Article ID 169321, 14 pages, 2009.
  14. D. Ji, Y. Tian, and W. Ge, “Positive solutions for one-dimensional p-Laplacian boundary value problems with sign changing nonlinearity,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 11, pp. 5406–5416, 2009. View at Publisher · View at Google Scholar
  15. Y. Sang and H. Su, “Positive solutions of nonlinear third-order m-point BVP for an increasing homeomorphism and homomorphism with sign-changing nonlinearity,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 288–300, 2009. View at Publisher · View at Google Scholar
  16. Y. Zhu and J. Zhu, “The multiple positive solutions for p-Laplacian multipoint BVP with sign changing nonlinearity on time scales,” Journal of Mathematical Analysis and Applications, vol. 344, no. 2, pp. 616–626, 2008. View at Publisher · View at Google Scholar
  17. Y. Sang, H. Su, and F. Xu, “Positive solutions of nonlinear m-point BVP for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales,” Computers & Mathematics with Applications, vol. 58, no. 2, pp. 216–226, 2009. View at Publisher · View at Google Scholar
  18. K. Q. Lan, “Multiple positive solutions of semilinear differential equations with singularities,” Journal of the London Mathematical Society, vol. 63, no. 3, pp. 690–704, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5, Academic Press, Boston, Mass, USA, 1988.