We study positive solutions to a steady state reaction diffusion equation arising in population dynamics, namely,

$ \begin{equation*} \label{abs} \left\lbrace \begin{matrix}-\Delta u = \lambda u(1-u) ;\; x\in\Omega\\ \frac{\partial u}{\partial \eta}+\gamma\sqrt{\lambda}[(A-u)^2+\epsilon]u = 0; \; x\in\partial \Omega \end{matrix} \right. \end{equation*} $

中文翻译：

---

关于外部矩阵敌对性和U型密度依赖扩散对扩散逻辑增长模型的影响

我们研究人口动态中产生的稳态反应扩散方程的正解，即

$ \ begin {equation *} \ label {abs} \ left \ lbrace \ begin {matrix}-\ Delta u = \ lambda u（1-u）; \; x \ in \ Omega \\ \ frac {\ partial u} {\ partial \ eta} + \ gamma \ sqrt {\ lambda} [（Au）^ 2 + \ epsuon] u = 0; \; x \ in \ partial \ Omega \ end {matrix} \ right。\ end {equation *} $