A Lotka-Volterra Competition Model with Cross-Diffusion | Zendy

Wenyan Chen | Zendy; Chen Ya | Zendy

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A Lotka-Volterra Competition Model with Cross-Diffusion

Author(s) -

Wenyan Chen,

Chen Ya

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/624352

Subject(s) - mathematics , competition (biology) , dirichlet boundary condition , homogeneous , competition model , diffusion , mathematical analysis , volterra equations , boundary value problem , nonlinear system , combinatorics , thermodynamics , quantum mechanics , profit (economics) , ecology , physics , microeconomics , economics , biology

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented

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