Uniqueness of the bistable traveling wave for mutualist species

Journal of Dynamics and Differential Equations

Volumn 13, Issue 1, 2001, Pages 147-183

  Huang, Wenzhang ^a  

^a The University of Alabama in Huntsville   (United States)

Author keywords

Fredholm operator, resolvent positive operator; Laplace transform; Reaction diffusion equations; Traveling wave

Indexed keywords

EID: 23044498797     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1009048616476     Document Type: Article

References (19)

1. Berman, A., and Plemmons, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics 9, SIAM, Philadelphia.
2. Chow, S. N., Lin, X. B., and Mallet-Paret, J. (1989). Transition layers for singularly perturbed delay differential equations with monotone nonlinearities. J. Dynam. Diff. Eq. 1, 3-43.
3. Conley, C. C., and Fife, P. (1982). Critical manifolds, traveling waves and an example from population genetics. J. Math. Bio. 14, 159-176.
4. 4. Trans. Am. Math. Soc. 286, 557-594.
5. Gardner, R. A. (1982). Existence and stability of travelling wave solutions of competition models: A degree theoretic approach. J. Diff. Eq. 44, 343-364.
6. Gardner, R. A. (1995). Review on Traveling Wave Solutions of Parabolic Systems by A. I. Volpert, V. A. Volpert, and V. A. Volpert. Bull. Am. Math. Soc. 32, 446-452.
7. Fife, P. C. (1979). Mathematical Aspects of Reacting and Diffusing Systems, Lect. Notes Biomath. 28, Springer-Verlag, New York.
8. Hale, J. K., and Lin, X. B. (1986). Heteroclinic orbits for retarded functional differential equations. J. Diff. Eq. 65, 175-202.
9. Hale, J. K., and Verduyn Lunel, S. M. (1993). Introduction to Functional Differential Equations, Springer-Verlag, New York.
10. Hartman, P. (1964). Ordinary Differential Equations, John Wiley and Sons, New York.
11. Kato, T. (1976). Perturbation Theory for Linear Operators, Springer-Verlag, Heidelberg.
12. Mallet-Paret, J. (1999). The Fredholm alternative for functional differential equations of mixed type. J. Dyn. Diff. Eq. 11, 1-48.
13. Mallet-Paret, J. (1999). The global structure of traveling waves in spatially discrete dynamical systems. J. Dyn. Diff. Eq. 11, 49-127.
14. Mischaikow, K. (1991). Traveling waves for a cooperative and a competitive-cooperative systems. In Shearer, M. (ed.), Viscous Profiles and Numerical Methods for Shock Waves, SIAM, Philadelphia, pp. 125-141.
15. Mischaikow, K., and Hutson, V. (1993). Traveling wave for mutualist species. SIAM J. Math. Anal. 24, 987-1008.
16. Mischaikow, K., and Reineck, J. (1993). Traveling waves in predator-prey systems. SIAM J. Math. Anal. 24, 1179-1214.
17. Murray, J. D. (1993). Mathematical Biology, Springer-Verlag, New York.
18. Thieme, H. R. (1998). Remarks on resolvent positive operators and their perturbation. Discrete Cont. Dynam. Syst. 4, 73-90.
19. Zeidler, E. (1993). Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorem, Springer-Verlag, New York.