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Some applications of the Łojasiewicz gradient inequality
On some spectral problems arising in dynamic populations
1. | Institut Elie Cartan, Nancy Université - CNRS, B.P. 239, 54 506 Vandoeuvre-les-Nancy, France |
2. | Institut Elie Cartan, Nancy Université - CNRS, B.P. 239, 54 506 Vandoeuvre-lès-Nancy, France, France |
References:
[1] |
S. Anita, W. E. Fitzgibbon and M. Langlais, Global existence and internal stabilization for a reaction-diffusion systems posed on non coincident spatial domains,, Discrete Contin. Dyn. Syst. Ser. B, 11 (2009), 805.
doi: 10.3934/dcdsb.2009.11.805. |
[2] |
H. Brézis, "Analyse Fonctionnelle,", Masson, (1983).
|
[3] |
G. Degla, An overview of semi-continuity results on the spectral radius and positivity,, J. Math. Anal. Appl., 338 (2008), 101.
doi: 10.1016/j.jmaa.2007.05.011. |
[4] |
A. Ducrot, V. Guyonne and M. Langlais, Some Remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains,, Discrete Contin. Dyn. Syst., 4 (2011), 67.
doi: 10.3934/dcdss.2011.4.67. |
[5] |
H. Egnell, Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 1.
|
[6] |
W. E. Fitzgibbon and M. Langlais, Simple models for the transmission of microparasites between host populations living on noncoincident spatial domains,, In, 1936 (2008), 115.
doi: 10.1007/978-3-540-78273-5_3. |
[7] |
A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,", Frontiers in Mathematics, (2006).
doi: 10.1007/3-7643-7706-2. |
[8] |
A. Henrot and M. Pierre, "Variation et optimisation de formes,", Math\'ematiques et Applications, 48 (2005).
doi: 10.1007/3-540-37689-5. |
[9] |
T. Kato, "Perturbation Theory for Linear Operators,", \textbf{132}, 132 (1966).
doi: 10.1007/978-3-642-66282-9. |
[10] |
M. Langlais, Some mathematical reaction-diffusion problems arising in population dynamics and posed on non coincident spatial domains,, Workshop, (2009), 22. Google Scholar |
show all references
References:
[1] |
S. Anita, W. E. Fitzgibbon and M. Langlais, Global existence and internal stabilization for a reaction-diffusion systems posed on non coincident spatial domains,, Discrete Contin. Dyn. Syst. Ser. B, 11 (2009), 805.
doi: 10.3934/dcdsb.2009.11.805. |
[2] |
H. Brézis, "Analyse Fonctionnelle,", Masson, (1983).
|
[3] |
G. Degla, An overview of semi-continuity results on the spectral radius and positivity,, J. Math. Anal. Appl., 338 (2008), 101.
doi: 10.1016/j.jmaa.2007.05.011. |
[4] |
A. Ducrot, V. Guyonne and M. Langlais, Some Remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains,, Discrete Contin. Dyn. Syst., 4 (2011), 67.
doi: 10.3934/dcdss.2011.4.67. |
[5] |
H. Egnell, Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 1.
|
[6] |
W. E. Fitzgibbon and M. Langlais, Simple models for the transmission of microparasites between host populations living on noncoincident spatial domains,, In, 1936 (2008), 115.
doi: 10.1007/978-3-540-78273-5_3. |
[7] |
A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,", Frontiers in Mathematics, (2006).
doi: 10.1007/3-7643-7706-2. |
[8] |
A. Henrot and M. Pierre, "Variation et optimisation de formes,", Math\'ematiques et Applications, 48 (2005).
doi: 10.1007/3-540-37689-5. |
[9] |
T. Kato, "Perturbation Theory for Linear Operators,", \textbf{132}, 132 (1966).
doi: 10.1007/978-3-642-66282-9. |
[10] |
M. Langlais, Some mathematical reaction-diffusion problems arising in population dynamics and posed on non coincident spatial domains,, Workshop, (2009), 22. Google Scholar |
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