中文摘要：

人口扩散模型在社会、经济等多方面有着广泛的应用,对其进行深入的研究有着一定的理论和实际意义。对一类人口扩散方程在其稳定状态下解的性态进行了讨论,其模型在稳定状态是一类半线性椭圆微分方程;对半线性椭圆微分方程的第三边值问题解的存在性和唯一性进行了研究。采用了上、下解方法,构造边值问题的上下解,证明了其非负解的存在性;并就2种不同的情况,利用强极值原理给出了解的唯一性条件。所得到的结论有一定的实际意义。

英文摘要：

The model of population diffusion is widely used in society and economy,and the futher research has certain theoretical and practical significance.In this paper the solution＇s character of population diffusion equation in their stable state is discussed.The existence and uniqueness of third value boundary problem of semi-linear elliptic equations is analyzed.With sup-solution and sub-solution methods,the existence of non-negative solution is presented and uniqueness conditions are given.The results have practical meaning.