About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 215617, 10 pages
http://dx.doi.org/10.1155/2012/215617
Research Article

Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

1School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
2College of Information Sciences and Technology, Hainan University, Haikou 570228, China

Received 27 September 2012; Accepted 13 October 2012

Academic Editor: Jifeng Chu

Copyright © 2012 Hailong Zhu and Shengjun Li. 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. R. P. Agarwal, D. O'Regan, and B. Yan, “Multiple positive solutions of singular Dirichlet second-order boundary-value problems with derivative dependence,” Journal of Dynamical and Control Systems, vol. 15, no. 1, pp. 1–26, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. F. M. Atici and G. S. Guseinov, “On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions,” Journal of Computational and Applied Mathematics, vol. 132, no. 2, pp. 341–356, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. A. Cabada and J. Cid, “Existence and multiplicity of solutions for a periodic Hill's equation with parametric dependence and singularities,” Abstract and Applied Analysis, vol. 2011, Article ID 545264, 19 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. Cabada and J. J. Nieto, “Extremal solutions of second order nonlinear periodic boundary value problems,” Applied Mathematics and Computation, vol. 40, no. 2, pp. 135–145, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. J. Chu, P. J. Torres, and M. Zhang, “Periodic solutions of second order non-autonomous singular dynamical systems,” Journal of Differential Equations, vol. 239, no. 1, pp. 196–212, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. J. Chu and M. Li, “Positive periodic solutions of Hill's equations with singular nonlinear perturbations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 1, pp. 276–286, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. A. Feichtinger, I. Rachůnková, S. Staněk, and E. Weinmüller, “Periodic BVPs in ODEs with time singularities,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 2058–2070, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. R. Graef, L. Kong, and H. Wang, “Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem,” Journal of Differential Equations, vol. 245, no. 5, pp. 1185–1197, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. X. Hao, L. Liu, and Y. Wu, “Existence and multiplicity results for nonlinear periodic boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 9-10, pp. 3635–3642, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. T. He, F. Yang, C. Chen, and S. Peng, “Existence and multiplicity of positive solutions for nonlinear boundary value problems with a parameter,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3355–3363, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. D. Jiang, “On the existence of positive solutions to second order periodic BVPs,” Acta Mathematica Sinica, vol. 18, pp. 31–35, 1998.
  12. D. Jiang, J. Chu, D. O'Regan, and R. P. Agarwal, “Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces,” Journal of Mathematical Analysis and Applications, vol. 286, no. 2, pp. 563–576, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. D. Jiang, J. Chu, and M. Zhang, “Multiplicity of positive periodic solutions to superlinear repulsive singular equations,” Journal of Differential Equations, vol. 211, no. 2, pp. 282–302, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. R. Ma, J. Xu, and X. Han, “Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 10, pp. 3379–3385, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. D. O'Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer Academic Publishers, Dodrecht, The Netherlands, 1997.
  16. I. Rachůnková, “Existence of two positive solution of a singular nonlinear periodic boundary value problem,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 24–34, 2000. View at Publisher · View at Google Scholar
  17. P. J. Torres, “Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, pp. 643–662, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. Z. Zhang and J. Wang, “On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations,” Journal of Mathematical Analysis and Applications, vol. 281, no. 1, pp. 99–107, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. M. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964.