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Positive periodic solution for generalized Basener-Ross model
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China |
This paper is devoted to the existence of at least one positive periodic solution for generalized Basener-Ross model with time-dependent coefficients. Our proof is based on Manásevich-Mawhin continuation theorem, Leray-Schauder alternative principle, fixed point theorem in cones. Moreover, we obtain that there are at least two positive periodic solutions for this model.
References:
[1] |
P. Amarasekare,
Effects of temperature on consumer-resource interactions, J. Animal Ecology, 84 (2015), 665-679.
doi: 10.1111/1365-2656.12320. |
[2] |
B. Basener and D. S. Ross,
Booming and crashing populations and Easter Island, SIAM J. Appl. Math., 65 (2004/05), 684-701.
doi: 10.1137/S0036139903426952. |
[3] |
M. Chen, M. Fan, X. Yuan and H. Zhu,
Effect of seasonal changing temperature on the growth of phytoplankton, Math. Biosci. Eng., 14 (2017), 1091-1117.
doi: 10.3934/mbe.2017057. |
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Z. Cheng and F. Li, Positive periodic solutions for a kind of second-order neutral differential equations with variable coefficient and delay, Mediterr. J. Math., 15 (2018), Art. 134, 19 pp.
doi: 10.1007/s00009-018-1184-y. |
[5] |
Z. Cheng and J. Ren,
Periodic solution for second order damped differential equations with attractive-repulsive singularities, Rocky Mountain J. Math., 48 (2018), 753-768.
doi: 10.1216/RMJ-2018-48-3-753. |
[6] |
A. Granas, R. B. Guenther and J. W. Lee,
Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures Appl., 70 (1991), 153-196.
|
[7] |
F. Güngör and P. J. Torres,
Integrability of the Basener-Ross model with time-dependent coefficients, SeMA J., 76 (2019), 485-493.
doi: 10.1007/s40324-019-00187-w. |
[8] |
A. Huppert, B. Blasius, R. Olinky and L. Stone,
A model for seasonal phytoplankton blooms, J. Theoret. Biol., 236 (2005), 276-290.
doi: 10.1016/j.jtbi.2005.03.012. |
[9] |
R. Manásevich and J. Mawhin,
Periodic solutions for nonlinear systems with $p$-Laplacian-like operators, J. Differential Equations, 145 (1998), 367-393.
doi: 10.1006/jdeq.1998.3425. |
[10] |
D. O'Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer Academic Publishers Group, Dordrecht, 1997.
doi: 10.1007/978-94-017-1517-1. |
[11] |
J. Ren, D. Zhu and H. Wang,
Spreading-vanishing dichotomy in information diffusion in online social networks with intervention, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 1843-1865.
doi: 10.3934/dcdsb.2018240. |
[12] |
Y. Wang, H. Lian and W. Ge,
Periodic solutions for a second order nonlinear functional differential equation, Appl. Math. Lett., 20 (2007), 110-115.
doi: 10.1016/j.aml.2006.02.028. |
[13] |
Y. Xu, D. Zhu and J. Ren, On a reaction-diffusion-advection system: Fixed boundary or free boundary, Electron. J. Qual. Theory Differ. Equ., (2018), Paper No. 26, 31 pp.
doi: 10.14232/ejqtde.2018.1.26. |
show all references
References:
[1] |
P. Amarasekare,
Effects of temperature on consumer-resource interactions, J. Animal Ecology, 84 (2015), 665-679.
doi: 10.1111/1365-2656.12320. |
[2] |
B. Basener and D. S. Ross,
Booming and crashing populations and Easter Island, SIAM J. Appl. Math., 65 (2004/05), 684-701.
doi: 10.1137/S0036139903426952. |
[3] |
M. Chen, M. Fan, X. Yuan and H. Zhu,
Effect of seasonal changing temperature on the growth of phytoplankton, Math. Biosci. Eng., 14 (2017), 1091-1117.
doi: 10.3934/mbe.2017057. |
[4] |
Z. Cheng and F. Li, Positive periodic solutions for a kind of second-order neutral differential equations with variable coefficient and delay, Mediterr. J. Math., 15 (2018), Art. 134, 19 pp.
doi: 10.1007/s00009-018-1184-y. |
[5] |
Z. Cheng and J. Ren,
Periodic solution for second order damped differential equations with attractive-repulsive singularities, Rocky Mountain J. Math., 48 (2018), 753-768.
doi: 10.1216/RMJ-2018-48-3-753. |
[6] |
A. Granas, R. B. Guenther and J. W. Lee,
Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures Appl., 70 (1991), 153-196.
|
[7] |
F. Güngör and P. J. Torres,
Integrability of the Basener-Ross model with time-dependent coefficients, SeMA J., 76 (2019), 485-493.
doi: 10.1007/s40324-019-00187-w. |
[8] |
A. Huppert, B. Blasius, R. Olinky and L. Stone,
A model for seasonal phytoplankton blooms, J. Theoret. Biol., 236 (2005), 276-290.
doi: 10.1016/j.jtbi.2005.03.012. |
[9] |
R. Manásevich and J. Mawhin,
Periodic solutions for nonlinear systems with $p$-Laplacian-like operators, J. Differential Equations, 145 (1998), 367-393.
doi: 10.1006/jdeq.1998.3425. |
[10] |
D. O'Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer Academic Publishers Group, Dordrecht, 1997.
doi: 10.1007/978-94-017-1517-1. |
[11] |
J. Ren, D. Zhu and H. Wang,
Spreading-vanishing dichotomy in information diffusion in online social networks with intervention, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 1843-1865.
doi: 10.3934/dcdsb.2018240. |
[12] |
Y. Wang, H. Lian and W. Ge,
Periodic solutions for a second order nonlinear functional differential equation, Appl. Math. Lett., 20 (2007), 110-115.
doi: 10.1016/j.aml.2006.02.028. |
[13] |
Y. Xu, D. Zhu and J. Ren, On a reaction-diffusion-advection system: Fixed boundary or free boundary, Electron. J. Qual. Theory Differ. Equ., (2018), Paper No. 26, 31 pp.
doi: 10.14232/ejqtde.2018.1.26. |
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