JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 76-84.doi: 10.6040/j.issn.1671-9352.0.2017.580
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DONG Ya-ying
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[1] DONG Yaying, LI Shanbing, LI Yanling. Multiplicity and uniqueness of positive solutions for a predator-prey model with C-M functional response[J]. Acta Applicandae Mathematicae, 2015, 139:187-206. [2] DONG Yaying, ZHANG Shunli, LI Shanbing, et al. Qualitative analysis of a predator-prey model with Crowley-Martin functional response[J]. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2015, 25(9):1550110(19 pages). [3] DU Yihong, LOU Yuan. Some uniqueness and exact multiplicity results for a predator-prey model[J]. Transactions of the American Mathematical Society, 1997, 349(6):2443-2475. [4] LI Lige. Coexistence theorems of steady-states for predator-prey interacting systems[J]. Transactions of the American Mathematical Society, 1988, 305(1):143-166. [5] LI Shanbing, WU Jianhua. Qualitative analysis of a predator-prey model with predator saturation and competition[J]. Acta Applicandae Mathematicae, 2016, 141:165-185. [6] HUFFAKER C B. Exerimental studies on predation: despersion factors and predator-prey oscilasions[J]. Hilgardia, 1958, 27:343-383. [7] BLAT J, BROWN K J. Global bifurcation of positive solutions in some systems of elliptic equations[J]. SIAM Journal on Mathematical Analysis, 1986, 17(6):1339-1353. [8] CASAL A, EILBECK J C, LÓPEZ-GÓMEZ J. Existence and uniqueness of coexistence states for a predator-prey model with diffusion[J]. Differential Integral Equations, 1994, 7(2):411-439. [9] DU Yihong, LOU Yuan. S-shaped global solution curve and Hopf bifurcation of positive solutions to a predator-prey model[J]. Journal of Differential Equations, 1998, 144(2):390-440. [10] DANCER E N, DU Yihong. Effects of certain degeneracies in the predator-prey model[J]. SIAM Journal on Mathematical Analysis, 2002, 34(2)292-314. [11] DANCER E N, DU Yihong. On a free boundary problem arising from population biology[J]. Indiana University Mathematics Journal, 2003, 52(1)51-67. [12] DU Yihong, HUANG Qingguang. Blow-up solutions for a class of semilinear elliptic and parabolic equations[J]. SIAM Journal on Mathematical Analysis, 1999, 31(1)1-18. [13] 叶其孝,李正元.反应扩散引论[M]. 北京:科学出版社, 1990. YE Qixiao, LI Zhengyuan. Introduction to reaction-diffusion equations[M]. Beijing: Science Press, 1990. [14] LÓPEZ-GÓMEZ J, SABINA de Lis J C. First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs[J]. Journal of Differential Equations, 1998, 148(1):47-64. [15] CRANDALL M G, RABINOWITZ P H. Bifurcation from simple eigenvalues[J]. Journal of Functional Analysis, 1971, 8:321-340. [16] LÓPEZ-GÓMEZ J. Spectral theory and nonlinear functional analysis[M]. Florida: Chapman and Hall/CRC Research Notes in Mathematics, 2001. [17] LI Shanbing, WU Jianhua, LIU Sanyang. Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone[J]. Calculus of Variations and Partial Differential Equations, 2017, 56(3):82(35 pages). |
[1] | ZHANG Li-na,LI Yan-ling,XIE Yu-long . Global bifurcation of a predator-prey system incorporating a prey refuge [J]. J4, 2007, 42(12): 110-115 . |
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