About this Journal Submit a Manuscript Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 869147, 11 pages
http://dx.doi.org/10.5402/2012/869147
Research Article

Existence of Alternate Steady States in a Phosphorous Cycling Model

1Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
2Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA

Received 20 January 2012; Accepted 8 February 2012

Academic Editors: J.-F. Colombeau, G. L. Karakostas, and P. Omari

Copyright © 2012 Dagny Butler 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. R. Carpenter, D. Ludwig, and W. A. Brock, “Management of eutrophication for lakes subject to potentially irreversible change,” Ecological Applications, vol. 9, no. 3, pp. 751–771, 1999. View at Publisher · View at Google Scholar
  2. M. Scheffer, W. Brock, and F. Westley, “Socioeconomic mechanisms preventing optimum use of ecosystem services: an interdisciplinary theoretical analysis,” Ecosystems, vol. 3, no. 5, pp. 451–471, 2000. View at Publisher · View at Google Scholar
  3. R. Aris, “On stability criteria of chemical reaction engineering,” Chemical Engineering Science, vol. 24, no. 1, pp. 149–169, 1969. View at Publisher · View at Google Scholar
  4. K. J. Brown, M. M. A. Ibrahim, and R. Shivaji, “S-shaped bifurcation curves,” Nonlinear Analysis, vol. 5, no. 5, pp. 475–486, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J.-P. Kernevez, G. Joly, M.-C. Duban, B. Bunow, and D. Thomas, “Hysteresis, oscillations, and pattern formation in realistic immobilized enzyme systems,” Journal of Mathematical Biology, vol. 7, no. 1, pp. 41–56, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. Ramaswamy and R. Shivaji, “Multiple positive solutions for classes of p-Laplacian equations,” Differential and Integral Equations, vol. 17, no. 11-12, pp. 1255–1261, 2004.
  7. E. Lee, S. Sasi, and R. Shivaji, “S-shaped bifurcation curves in ecosystems,” Journal of Mathematical Analysis and Applications, vol. 381, no. 2, pp. 732–741, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. Amann, “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,” SIAM Review, vol. 18, no. 4, pp. 620–709, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Shivaji, “A remark on the existence of three solutions via sub-super solutions,” in Nonlinear Analysis and Applications, vol. 109 of Lecture Notes in Pure and Applied Mathematics, pp. 561–566, Dekker, New York, NY, USA, 1987. View at Zentralblatt MATH
  10. J. Jiang and J. Shi, “Bistability dynamics in some structured ecological models,” in Spatial Ecology, R. S. Cantrell, C. Cosner, and S. Ruan, Eds., Mathematical and Computational Biology, pp. 33–62, Chapman & Hall/CRC, 2009.
  11. R. Shivaji, “A remark on the existence of three solutions via sub-super solutions, Nonlinear Analysis and Applications- Ed V,” Lakshmikantham, pp. 561–566, 1987.
  12. T. Laetsch, “The number of solutions of a nonlinear two point boundary value problem,” Indiana University Mathematics Journal, vol. 20, pp. 1–13, 1970. View at Publisher · View at Google Scholar