Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species

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Erratum to: "On a functional satisfying a weak Palais-Smale condition"

November 2014, 34(11): 4989-4995. doi: 10.3934/dcds.2014.34.4989

Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species

Xinfu Chen ^1, , King-Yeung Lam ^2, and Yuan Lou ^3,

1.	Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.	Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States
3.	Department of Mathematics, Mathematical Bioscience Institute, Ohio State University, Columbus, Ohio 43210

Received December 2013 Revised December 2013 Published May 2014

Abstract
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We provide a corrected proof of [4, Theorem 2.2], which preserves the validity of the theorem exactly under those assumptions as stated in the original paper.

Keywords: exclusion, evolution of dispersal., Directed movement, competing species, reaction-diffusion-advection.

Mathematics Subject Classification: Primary: 35J57, 35B40; Secondary: 92D4.

Citation: Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989

References:

[1]	H. Amann and J. Lopez-Gomez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Diff. Eqns., 146 (2002), 336-374. doi: 10.1006/jdeq.1998.3440.
[2]	F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quarterly, 3 (1995), 379-397.
[3]	S. Cano-Casanova and J. Lopez-Gomez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems, J. Diff. Eqns., 178 (2002), 123-211. doi: 10.1006/jdeq.2000.4003.
[4]	X. Chen, K.-Y. Lam and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competiting species, Discrete Cont. Dyn. Sys. A, 32 (2012), 3841-3859. doi: 10.3934/dcds.2012.32.3841.
[5]	D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equation of Second Order, $2^{nd}$ Ed., Springer-Verlag, Berlin, 1983.

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References:

[1]	H. Amann and J. Lopez-Gomez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Diff. Eqns., 146 (2002), 336-374. doi: 10.1006/jdeq.1998.3440.
[2]	F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quarterly, 3 (1995), 379-397.
[3]	S. Cano-Casanova and J. Lopez-Gomez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems, J. Diff. Eqns., 178 (2002), 123-211. doi: 10.1006/jdeq.2000.4003.
[4]	X. Chen, K.-Y. Lam and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competiting species, Discrete Cont. Dyn. Sys. A, 32 (2012), 3841-3859. doi: 10.3934/dcds.2012.32.3841.
[5]	D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equation of Second Order, $2^{nd}$ Ed., Springer-Verlag, Berlin, 1983.

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