一类具交错扩散的互惠模型的共存解

The Coexistence of a System Describing a Mutualistic Model and with Cross-Diffusions

研究了Dirichlet边界条件下具交错扩散的两种群互惠模型.采用上下解方法,结合Schauder不动点理论,给出了问题共存解存在的充分条件.进一步,利用单调迭代序列的方法构造出问题的共存解.结果表明,当交错扩散相对弱时,问题至少存在一共存解.

This paper deals with a two-species mutualistic model with cross-diffusions under Dirichlet conditions. With the method of upper and lower solutions and fixed point theorem, the conditions of the existence of coexistence solutions to the above system are gived. Furthermore, by making use of its associated monotone iterations, the coexistence solutions of this system are constructed. Our results show that the system possesses at least one coexistence state if cross-diffusions are weak.