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Positive steady state solutions of a plant-pollinator model with diffusion
1. | Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China, China, China |
References:
[1] |
J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, Journal of Animal Ecology, 44 (1975), 331-340.
doi: 10.2307/3866. |
[2] |
J. Blat and K. J. Brown, Global bifurcation of positive solutions in some systems of elliptic equations, SIAM Journal on Mathematical Analysis, 17 (1986), 1339-1353.
doi: 10.1137/0517094. |
[3] |
R. S. Cantrell and C. Cosner, On the steady-state problem for the Volterra-Lotka competition model with diffusion, Houston J. Math., 13 (1987), 337-352. |
[4] |
C. S. Cassanova, Existece and strueture of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems, Nonlinear Analysis: Theory, Methods & Applications, 49 (2002), 361-430.
doi: 10.1016/S0362-546X(01)00116-X. |
[5] |
P. R. Crane, E. M. Friis and K. R. Pedersen, Lower cretaceous angiosperm flowers: Fossil evidence on early radiation of dicotyledons, Science, 232 (1986), 852-854.
doi: 10.1126/science.232.4752.852. |
[6] |
P. R. Crane, E. M. Friis and K. R. Pedersen, The origin and early diversification of angiosperms, Nature, 374 (1994), 27-33.
doi: 10.1038/374027a0. |
[7] |
E. N. Daneer, On the indices of fixed poins of mappings in cones and applications, Journal of Mathematical Analysis and Applications, 91 (1983), 131-151.
doi: 10.1016/0022-247X(83)90098-7. |
[8] |
C. Darwin, The Origin of Species, Penguin Books, London, UK. 1859. |
[9] |
C. Darwin, The Effects of Cross and Self-Fertilisation in the Vegetable Kingdom, Appelton, New York, 1876.
doi: 10.1017/CBO9780511694202. |
[10] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for trophic interaction, Ecology, 56 (1975), 881-892.
doi: 10.2307/1936298. |
[11] |
Y. H. Du and Y. Lou, Some uniqueness and exact multiplicity results for a predator-prey model, Trans. Amer. Math. Soc., 349 (1997), 2443-2475.
doi: 10.1090/S0002-9947-97-01842-4. |
[12] |
M. A. Fishman and L. Hadany, Plant-pollinator population dynamics, Theoretical Population Biology, 78 (2010), 270-277.
doi: 10.1016/j.tpb.2010.08.002. |
[13] |
S. R. Jang, Dynamics of herbivore-plant-pollinator models, Journal of Mathematical Biology, 44 (2002), 129-149.
doi: 10.1007/s002850100117. |
[14] |
L. G. Li, Coexistence theorems of steady states for predator-prey interacting systems, Transactions of the American Mathematical Society, 305 (1988), 143-166.
doi: 10.1090/S0002-9947-1988-0920151-1. |
[15] |
L. Lou and S. Martínez and P. Poláčik, Loops and branches of coexistence states in a Lotka-Volterra competition model, Journal of Differential Equations, 230 (2006), 720-742.
doi: 10.1016/j.jde.2006.04.005. |
[16] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1994.
doi: 10.1007/978-1-4612-0873-0. |
[17] |
J. M. Soberon and C. M. Del Rio, The dynamics of a plant-pollinator interaction, Journal of Theoretical Biology, 91(1981), 363-378.
doi: 10.1016/0022-5193(81)90238-1. |
[18] |
Y. Wang, H. Wu and S. Sun, Persistence of pollination mutualisms in plant-pollinator-robber systems, Theoretical Population Biology, 81 (2012), 243-250.
doi: 10.1016/j.tpb.2012.01.004. |
[19] |
L. J. Wang and H. L. Jiang, Properties and numerical simulations of positive solutions for a variable-territory model, Applied Mathematics and Computation, 236 (2014), 647-662.
doi: 10.1016/j.amc.2014.03.080. |
show all references
References:
[1] |
J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, Journal of Animal Ecology, 44 (1975), 331-340.
doi: 10.2307/3866. |
[2] |
J. Blat and K. J. Brown, Global bifurcation of positive solutions in some systems of elliptic equations, SIAM Journal on Mathematical Analysis, 17 (1986), 1339-1353.
doi: 10.1137/0517094. |
[3] |
R. S. Cantrell and C. Cosner, On the steady-state problem for the Volterra-Lotka competition model with diffusion, Houston J. Math., 13 (1987), 337-352. |
[4] |
C. S. Cassanova, Existece and strueture of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems, Nonlinear Analysis: Theory, Methods & Applications, 49 (2002), 361-430.
doi: 10.1016/S0362-546X(01)00116-X. |
[5] |
P. R. Crane, E. M. Friis and K. R. Pedersen, Lower cretaceous angiosperm flowers: Fossil evidence on early radiation of dicotyledons, Science, 232 (1986), 852-854.
doi: 10.1126/science.232.4752.852. |
[6] |
P. R. Crane, E. M. Friis and K. R. Pedersen, The origin and early diversification of angiosperms, Nature, 374 (1994), 27-33.
doi: 10.1038/374027a0. |
[7] |
E. N. Daneer, On the indices of fixed poins of mappings in cones and applications, Journal of Mathematical Analysis and Applications, 91 (1983), 131-151.
doi: 10.1016/0022-247X(83)90098-7. |
[8] |
C. Darwin, The Origin of Species, Penguin Books, London, UK. 1859. |
[9] |
C. Darwin, The Effects of Cross and Self-Fertilisation in the Vegetable Kingdom, Appelton, New York, 1876.
doi: 10.1017/CBO9780511694202. |
[10] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for trophic interaction, Ecology, 56 (1975), 881-892.
doi: 10.2307/1936298. |
[11] |
Y. H. Du and Y. Lou, Some uniqueness and exact multiplicity results for a predator-prey model, Trans. Amer. Math. Soc., 349 (1997), 2443-2475.
doi: 10.1090/S0002-9947-97-01842-4. |
[12] |
M. A. Fishman and L. Hadany, Plant-pollinator population dynamics, Theoretical Population Biology, 78 (2010), 270-277.
doi: 10.1016/j.tpb.2010.08.002. |
[13] |
S. R. Jang, Dynamics of herbivore-plant-pollinator models, Journal of Mathematical Biology, 44 (2002), 129-149.
doi: 10.1007/s002850100117. |
[14] |
L. G. Li, Coexistence theorems of steady states for predator-prey interacting systems, Transactions of the American Mathematical Society, 305 (1988), 143-166.
doi: 10.1090/S0002-9947-1988-0920151-1. |
[15] |
L. Lou and S. Martínez and P. Poláčik, Loops and branches of coexistence states in a Lotka-Volterra competition model, Journal of Differential Equations, 230 (2006), 720-742.
doi: 10.1016/j.jde.2006.04.005. |
[16] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1994.
doi: 10.1007/978-1-4612-0873-0. |
[17] |
J. M. Soberon and C. M. Del Rio, The dynamics of a plant-pollinator interaction, Journal of Theoretical Biology, 91(1981), 363-378.
doi: 10.1016/0022-5193(81)90238-1. |
[18] |
Y. Wang, H. Wu and S. Sun, Persistence of pollination mutualisms in plant-pollinator-robber systems, Theoretical Population Biology, 81 (2012), 243-250.
doi: 10.1016/j.tpb.2012.01.004. |
[19] |
L. J. Wang and H. L. Jiang, Properties and numerical simulations of positive solutions for a variable-territory model, Applied Mathematics and Computation, 236 (2014), 647-662.
doi: 10.1016/j.amc.2014.03.080. |
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