Positive solutions bifurcating from zero solution in a Lotka-Volterra competitive system with cross-diffusion effects |
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Authors: | Cun-hua Zhang Xiang-ping Yan |
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Institution: | Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China |
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Abstract: | A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of
the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function
theorem and the Lyapunov-Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution
is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated
characteristic equation. |
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Keywords: | Lotka-Volterra competitive system Cross-Diffusion Positive solution Steady state bifurcation Stability |
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