中文摘要：

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．

英文摘要：

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 princi- ple. 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.