- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 869147, 11 pages
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.
- 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.
- 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.
- R. Aris, “On stability criteria of chemical reaction engineering,” Chemical Engineering Science, vol. 24, no. 1, pp. 149–169, 1969.
- K. J. Brown, M. M. A. Ibrahim, and R. Shivaji, “S-shaped bifurcation curves,” Nonlinear Analysis, vol. 5, no. 5, pp. 475–486, 1981.
- 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.
- 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.
- 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.
- H. Amann, “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,” SIAM Review, vol. 18, no. 4, pp. 620–709, 1976.
- 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.
- 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.
- 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.
- T. Laetsch, “The number of solutions of a nonlinear two point boundary value problem,” Indiana University Mathematics Journal, vol. 20, pp. 1–13, 1970.