CAJ | 학술논문

研究了一类带有交叉扩散项的捕食-食饵模型的Dirichlet 问题正解的存在性。利用极大值原理得到了正解的先验估计，借助Crandall-Rabinowitz 分歧理论，得到了局部分歧正解的存在性，并将局部分歧延拓为全局分歧，从而得到正解存在的充分条件。最终结果表明，在一定条件下捕食者与食饵可以共存。
연구료일류대유교차확산항적포식-식이모형적Dirichlet 문제정해적존재성。이용겁대치원리득도료정해적선험고계，차조Crandall-Rabinowitz 분기이론，득도료국부분기정해적존재성，병장국부분기연탁위전국분기，종이득도정해존재적충분조건。최종결과표명，재일정조건하포식자여식이가이공존。
The existence of positive solutions for Dirichlet problem with a predator-prey model with cross-diffu-sion is studied .A priori estimate of positive solution was got by using maximum principle and the existence of positive solutions was obtained with the help of Crandall-Rabinowitz bifurcation theory ,then the local bifurca-tion solution was developed to the global one ,thus the sufficient conditions of positive solutions were obtained . It has shown that predator and prey can coexist under certain conditions .