一类具有内部存储的非均匀恒化器模型的共存解

本文研究一类具有内部存储的非均匀恒化器模型正平衡解的存在性.由于模型中比率项的奇性,通常的线性化方法、分歧理论等均不适用.为克服比率项的奇性,首先建立模型正平衡解细致的先验估计,该估计表明模型的正平衡解含于一个特殊的锥内.然后借助于一类非线性特征值问题的主特征值及锥上的不动点指标理论给出了模型正平衡解存在的充分条件.

Coexistence Solutions of the Unstirred Chemostat Model with Internal Storage

The existence of positive steady state solutions of an unstirred chemostat model with internal storage is studied. Due to the singularity arising from the ratio terms in this model, standard technique such as linearization and bifurcation can not be applied here. In order to overcome the mathematical difficulties caused by the singularity in the ratio terms, the sharp priori estimates for positive steady state solutions of the system are established firstly, which ensure that all positive steady state solutions of the system belong to a special cone. Secondly, some sufficient conditions for the existence of positive steady state solutions are given by using the principle eigenvalues of associated nonlinear eigenvalue problems and the degree theory in the special cone.