具有饱和项的互惠模型正解的存在性

Existence of Positive Solutions for a Cooperative Model with Saturation

研究了Volterra Lotka具有饱和项的互惠模型的平衡态方程,主要考虑了单种群具有饱和项的互惠模型.利用正的紧线性微分算子的谱性质和锥映象不动点指标,结合极值原理,上下解方法,得到了具有饱和项的互惠模型正解存在的充分条件.结果表明,这些正解的存在性与一类Schrodinger型微分算子的谱性质密切相关.

The steadystate equation of a kind of the VolterraLotka for a cooperative model with saturation is studied. A cooperative system with a saturating interaction term for one species is mainly concerned. By means of the spectral properties of positive compact linear differential operators and fixed points index of compact maps in cones, combining with maximum principles, lowerupper solutions methods, sufficient conditions of positive solutions for a cooperative system with saturation are obtained. The results show that the positive solutions are closely related to the spectral properties of certain differential operators of Schrodinger type.