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Axisymmetry of locally bounded solutions to an EulerLagrange system of the weighted HardyLittlewoodSobolev inequality
The diffusive logistic model with a free boundary and seasonal succession
1.  Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China, and Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada 
2.  Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7 
References:
[1] 
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" Lecture Notes in Math., 446, Springer, Berlin, (1975), 549. 
[2] 
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 (1978), 3376. doi: 10.1016/00018708(78)901305. 
[3] 
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model,, Networks and Heterogeneous Media, (). 
[4] 
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778800. doi: 10.1137/S0036141099351693. 
[5] 
D. L. DeAngelis, J. C. Trexler and D. D. Donalson, "Competition Dynamics in a Seasionally Varying Wetland," Chapter 1, 113, in "Spatial Ecology" (Eds. S. Cantrell, C. Cosner and S. Ruan), CRC Press, Chapman and Hall, (2009). 
[6] 
Y. Du and Z. M. Guo, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary II, J. Differential Equations, 250 (2011), 43364366. doi: 10.1016/j.jde.2011.02.011. 
[7] 
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in timeperiodic environment, preprint, 2011. 
[8] 
Y. Du and Z. G. Lin, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377405. doi: 10.1137/090771089. 
[9] 
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition, Ecology, 69 (1988), 14391453. 
[10] 
S.B. Hsu and X.Q. Zhao, A LotkaVolterra competition model with seasonal succession, J. Math. Biol., 64 (2012), 109130. doi: 10.1007/s0028501104086. 
[11] 
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra and interspecific competition in a Daphnia assemblage, Ecology, 76 (1995), 22782294. 
[12] 
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc. Providence, RI, 1968. 
[13] 
X. Liang, Y. Yi and X.Q. Zhao, Spreading speeds and traveling waves for periodic evolution systems, J. Differential Equations, 231 (2006), 5777. doi: 10.1016/j.jde.2006.04.010. 
[14] 
X. Liang and X.Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 140. doi: 10.1002/cpa.20154. 
[15] 
Z. G. Lin, A free boundary problem for a predatorprey model, Nonlinearity, 20 (2007), 18831892. doi: 10.1088/09517715/20/8/004. 
[16] 
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, American Naturalist, 157 (2001), 170187. 
[17] 
T. R. Malthus, "An Essay on the Principle of Population," 1798. Printed for J. Johnson in St. Pauls ChurchYard, 1998. 
[18] 
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151186. doi: 10.1007/BF03167042. 
[19] 
G. Nadin, The principal eigenvalue of a spacetime periodic parabolic operator, Ann. Mat. Pura Appl., 188 (2009), 269295. doi: 10.1007/s1023100800754. 
[20] 
R. Peng and D. Wei, The periodicparabolic logistic equation on $\R^N$, Discrete and Continuous Dyn. Syst. Series A, 32 (2012), 619641. 
[21] 
H. F. Weinberger, Longtime behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), 353396. doi: 10.1137/0513028. 
[22] 
X.Q. Zhao, "Dynamical Systems in Population Biology," SpringerVerlag, New York, 2003. 
show all references
References:
[1] 
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" Lecture Notes in Math., 446, Springer, Berlin, (1975), 549. 
[2] 
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 (1978), 3376. doi: 10.1016/00018708(78)901305. 
[3] 
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model,, Networks and Heterogeneous Media, (). 
[4] 
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778800. doi: 10.1137/S0036141099351693. 
[5] 
D. L. DeAngelis, J. C. Trexler and D. D. Donalson, "Competition Dynamics in a Seasionally Varying Wetland," Chapter 1, 113, in "Spatial Ecology" (Eds. S. Cantrell, C. Cosner and S. Ruan), CRC Press, Chapman and Hall, (2009). 
[6] 
Y. Du and Z. M. Guo, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary II, J. Differential Equations, 250 (2011), 43364366. doi: 10.1016/j.jde.2011.02.011. 
[7] 
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in timeperiodic environment, preprint, 2011. 
[8] 
Y. Du and Z. G. Lin, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377405. doi: 10.1137/090771089. 
[9] 
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition, Ecology, 69 (1988), 14391453. 
[10] 
S.B. Hsu and X.Q. Zhao, A LotkaVolterra competition model with seasonal succession, J. Math. Biol., 64 (2012), 109130. doi: 10.1007/s0028501104086. 
[11] 
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra and interspecific competition in a Daphnia assemblage, Ecology, 76 (1995), 22782294. 
[12] 
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc. Providence, RI, 1968. 
[13] 
X. Liang, Y. Yi and X.Q. Zhao, Spreading speeds and traveling waves for periodic evolution systems, J. Differential Equations, 231 (2006), 5777. doi: 10.1016/j.jde.2006.04.010. 
[14] 
X. Liang and X.Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 140. doi: 10.1002/cpa.20154. 
[15] 
Z. G. Lin, A free boundary problem for a predatorprey model, Nonlinearity, 20 (2007), 18831892. doi: 10.1088/09517715/20/8/004. 
[16] 
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, American Naturalist, 157 (2001), 170187. 
[17] 
T. R. Malthus, "An Essay on the Principle of Population," 1798. Printed for J. Johnson in St. Pauls ChurchYard, 1998. 
[18] 
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151186. doi: 10.1007/BF03167042. 
[19] 
G. Nadin, The principal eigenvalue of a spacetime periodic parabolic operator, Ann. Mat. Pura Appl., 188 (2009), 269295. doi: 10.1007/s1023100800754. 
[20] 
R. Peng and D. Wei, The periodicparabolic logistic equation on $\R^N$, Discrete and Continuous Dyn. Syst. Series A, 32 (2012), 619641. 
[21] 
H. F. Weinberger, Longtime behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), 353396. doi: 10.1137/0513028. 
[22] 
X.Q. Zhao, "Dynamical Systems in Population Biology," SpringerVerlag, New York, 2003. 
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