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Volterra-Lotka Model of Steady State with Diffusion
Li Dongsheng,Huang Aixiang
(Xi'an Jiaotong University, Xi'an 710049, China)
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Abstract: By using Green's formula, Sobolevi nequality and Yong inequality, a piori estimate for the solutions of the Volterra-Lotka model of steady state with diffusion is given. Using the fixed point index theory,the indices of the trival and semi-trival solutions are computed. Form this,the coexistence of the model is proved as the sum of the indices of the trival and semitrival solutions is not equal tol.
Keywords: Volterra-Lotka model;priori estimate;fixed point index; coexistence