一类带饱和项互惠模型平衡态正解的存在性

The existence of positive solutions of the steady state system for cooperative model with saturation terms

研究了一类两个物种同时带有饱和项的互惠模型在第一边界值条件下的平衡态正解的存在性.首先用单调解的方法给出了此解的先验估计,然后利用局部分歧理论研究了在λ1-c<a<λ1和a>λ1两种情况下模型分别在两个半平凡解上出现的局部分歧现象,并证明了分别在分歧点(β,0,θβ)和(b′,θa,0)附近存在正解;最后利用全局分歧理论研究了其整体分歧,从而证明了这两种情况下模型存在平衡态正解.

The existence of positive solutions of the steady-state system are discussed for cooperative model with saturating terms for two species under the first boundary conditions. First, the prior estimate of the solutions is given by the monotone method; by means of local bifurcation theory, the system bifurcations at two semi-trivial solutions for two cases（ λ1 - c 〈 a 〈 λ 1 and a 〉 λ 1 ） are studied, respectively. It is proved that positive solutions exist in some neighborhoods of （β,0,θβ） and （b＇, θa, 0 ）, respectively. Finally, the global bifurcations are investigated by the global bifurcation theory, and the existence of positive solutions of the steady-state system for the two cases are obtained accordingly.