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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 714248, 18 pages
A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 13 December 2010; Revised 13 February 2011; Accepted 24 February 2011
Academic Editor: Elena Braverman
Copyright © 2011 Jiebao Sun 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.
- J. A. Cui, “Global asymptotic stability in -species cooperative system with time delays,” Systems Science and Mathematical Sciences, vol. 7, no. 1, pp. 45–48, 1994.
- D. Hu and Z. Zhang, “Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1115–1121, 2010.
- K. I. Kim and Z. Lin, “A degenerate parabolic system with self-diffusion for a mutualistic model in ecology,” Nonlinear Analysis: Real World Applications, vol. 7, no. 4, pp. 597–609, 2006.
- Y. Lou, T. Nagylaki, and W.-M. Ni, “On diffusion-induced blowups in a mutualistic model,” Nonlinear Analysis: Theory, Methods & Applications, vol. 45, no. 3, pp. 329–342, 2001.
- Z. Lin, J. Liu, and M. Pedersen, “Periodicity and blowup in a two-species cooperating model,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 479–486, 2011.
- C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992.
- Z. Y. Lu and Y. Takeuchi, “Permanence and global stability for cooperative Lotka-Volterra diffusion systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 19, no. 10, pp. 963–975, 1992.
- J. Sun, B. Wu, and D. Zhang, “Asymptotic behavior of solutions of a periodic diffusion equation,” Journal of Inequalities and Applications, vol. 2010, Article ID 597569, 12 pages, 2010.
- S. Ahmad and A. C. Lazer, “Asymptotic behaviour of solutions of periodic competition diffusion system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 13, no. 3, pp. 263–284, 1989.
- A. Tineo, “Existence of global coexistence state for periodic competition diffusion systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 19, no. 4, pp. 335–344, 1992.
- K. Gopalsamy, “Global asymptotic stability in a periodic Lotka-Volterra system,” Journal of the Australian Mathematical Society. Series B, vol. 27, no. 1, pp. 66–72, 1985.
- J. López-Gómez, “Positive periodic solutions of Lotka-Volterra reaction-diffusion systems,” Differential and Integral Equations, vol. 5, no. 1, pp. 55–72, 1992.
- J. J. Morgan and S. L. Hollis, “The existence of periodic solutions to reaction-diffusion systems with periodic data,” SIAM Journal on Mathematical Analysis, vol. 26, no. 5, pp. 1225–1232, 1995.
- C. V. Pao, “Periodic solutions of parabolic systems with nonlinear boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 234, no. 2, pp. 695–716, 1999.
- C. Tian and Z. Lin, “Periodic solutions of reaction diffusion systems in a half-space domain,” Nonlinear Analysis: Real World Applications, vol. 9, no. 3, pp. 811–821, 2008.
- K. J. Brown and P. Hess, “Positive periodic solutions of predator-prey reaction-diffusion systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 16, no. 12, pp. 1147–1158, 1991.
- J.-B. Sun, C.-H. Jin, and Y.-Y. Ke, “Existence of non-trivial nonnegative periodic solutions for a nonlinear diffusion system,” Northeastern Mathematical Journal, vol. 23, no. 2, pp. 167–175, 2007.
- J.-B. Sun, “Asymptotic bounds for solutions of a periodic reaction diffusion system,” Applied Mathematics E-Notes, vol. 10, pp. 128–135, 2010.
- J. Yin and Y. Wang, “Asymptotic behaviour of solutions for nonlinear diffusion equation with periodic absorption,” in Partial Differential Equations and Their Applications (Wuhan, 1999), pp. 305–308, World Scientific, River Edge, NJ, USA, 1999.
- A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, vol. 23 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1967.
- Z. Q. Wu, J. X. Yin, and C. P. Wang, Introduction to Elliptic and Parabolic Equations, Scientific Publications, Beijing, China, 2003.
- Z. Wu, J. Zhao, J. Yin, and H. Li, Nonlinear Diffusion Equations, World Scientific, River Edge, NJ, USA, 2001.
- E. DiBenedetto, “Continuity of weak solutions to a general porous medium equation,” Indiana University Mathematics Journal, vol. 32, no. 1, pp. 83–118, 1983.
- M. M. Porzio and V. Vespri, “Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations,” Journal of Differential Equations, vol. 103, no. 1, pp. 146–178, 1993.
- P. Hess, M. A. Pozio, and A. Tesei, “Time periodic solutions for a class of degenerate parabolic problems,” Houston Journal of Mathematics, vol. 21, no. 2, pp. 367–394, 1995.