Positive solutions for a general Gause-type predator-prey model with monotonic functional response

Abstract and Applied Analysis

Volumn 2011, Issue , 2011, Pages

  Zhang, Guohong ^a   Wang, Xiaoli ^a  

^a SOUTHWEST UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053638826     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2011/547060     Document Type: Article

References (27)

1. Peng R., Shi J., Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: strong interaction case Journal of Differential Equations 2009 247 3 866 886
2. Yi F., Wei J., Shi J., Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system Journal of Differential Equations 2009 246 5 1944 1977
3. Ko W., Ryu K., A qualitative study on general Gause-type predator-prey models with non-monotonic functional response Nonlinear Analysis: Real World Applications 2009 10 4 2558 2573
4. Ko W., Ryu K., Coexistence states of a predator-prey system with non-monotonic functional response Nonlinear Analysis: Real World Applications 2007 8 3 769 786 (Pubitemid 46097506)
5. Ko W., Ryu K., A qualitative study on general Gause-type predator-prey models with constant diffusion rates Journal of Mathematical Analysis and Applications 2008 344 1 217 230
6. Cantrell R. S., Cosner C., Spatial Ecology via Reaction-Diffusion Equations 2003 Chichester, UK John Wiley Sons xvi+411 Wiley Series in Mathematical and Computational Biology
7. Pao C. V., Nonlinear Parabolic and Elliptic Equations 1992 New York, NY, USA Plenum Press xvi+777
8. Ma T., Wang S., Bifurcation Theory and Applications 2005 53 Hackensack, NJ, USA World Scientific xiv+375 World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises
9. Dancer E. N., On positive solutions of some pairs of differential equations Transactions of the American Mathematical Society 1984 284 2 729 743
10. Dancer E. N., On positive solutions of some pairs of differential equations. II Journal of Differential Equations 1985 60 2 236 258
11. Dancer E. N., On the indices of fixed points of mappings in cones and applications Journal of Mathematical Analysis and Applications 1983 91 1 131 151
12. Dancer E. N., Bifurcation from simple eigenvalues and eigenvalues of geometric multiplicity one The Bulletin of the London Mathematical Society 2002 34 5 533 538 (Pubitemid 36224166)
13. Li L., Coexistence theorems of steady states for predator-prey interacting systems Transactions of the American Mathematical Society 1988 305 1 143 166
14. Pang P. Y. H., Wang M., Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion Proceedings of the London Mathematical Society 2004 88 1 135 157 (Pubitemid 38284647)
15. Peng R., Wang M., On multiplicity and stability of positive solutions of a diffusive prey-predator model Journal of Mathematical Analysis and Applications 2006 316 1 256 268 (Pubitemid 43040316)
16. Zeng X., A ratio-dependent predator-prey model with diffusion Nonlinear Analysis: Real World Applications 2007 8 4 1062 1078 (Pubitemid 46551821)
17. Fan Y.-H., Li W.-T., Global asymptotic stability of a ratio-dependent predator-prey system with diffusion Journal of Computational and Applied Mathematics 2006 188 2 205 227 (Pubitemid 41705818)
18. Du Y., Lou Y., Qualitative behaviour of positive solutions of a predator-prey model: effects of saturation Proceedings of the Royal Society of Edinburgh. Section A 2001 131 2 321 349
19. Du Y., Lou Y., Some uniqueness and exact multiplicity results for a predator-prey model Transactions of the American Mathematical Society 1997 349 6 2443 2475 (Pubitemid 127745357)
20. Du Y., Lou Y., S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model Journal of Differential Equations 1998 144 2 390 440 (Pubitemid 128347808)
21. Crandall M. G., Rabinowitz P. H., Bifurcation from simple eigenvalues Journal of Functional Analysis 1971 8 321 340
22. Lpez-Gmez J., Molina-Meyer M., Bounded components of positive solutions of abstract fixed point equations: mushrooms, loops and isolas Journal of Differential Equations 2005 209 2 416 441 (Pubitemid 40030551)
23. Cano-Casanova S., Existence and structure of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems Nonlinear Analysis: Theory, Methods Applications 2002 49 3 361 430 (Pubitemid 34100267)
24. Cano-Casanova S., Lpez-Gmez J., Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems Journal of Differential Equations 2002 178 1 123 211
25. Lpez-Gmez J., Spectral Theory and Nonlinear Functional Analysis 2001 426 Boca Raton, Fla, USA Chapman Hall/CRC xii+265 Chapman Hall/CRC Research Notes in Mathematics
26. Lpez-Gmez J., The steady states of a non-cooperative model of nuclear reactors Journal of Differential Equations 2009 246 1 358 372
27. Rabinowitz P. H., Some global results for nonlinear eigenvalue problems Journal of Functional Analysis 1971 7 487 513