分析一类具有弹性增长的非线性尺度结构种群系统模型, 个体生死率对密度制约的响应不同. 运用耦合上下解方法、比较原理和延拓思想确立了模型非负有界解的存在唯一性;给出了正平衡态的存在性判据和表达式, 导出了平衡态的特征方程, 获得了稳定性判别准则, 在不考虑死亡率的密度制约时还得到了正平衡态稳定性阈值. 其结果为种群生存分析、状态逼近和控制问题研究奠定基础.

This paper analyzes a class of nonlinear size-structured population model with elastic growth, in which the fertility and mortality have different responses to the density-dependence. The existence of unique nonnegative solution to the model is proved by means of coupled upper and lower solutions and comparison principle. Furthermore, we establish conditions for the existence and stability of positive steady states, and derives the corresponding characteristic equation. For the case of density-independent mortality, we find the threshold of parameters for the stability of nontrivial equilibrium. The results obtained pave a sound way for the investigation of persistence, approximation and control problems.