作　　者： (潘宇洋）; (王晓云）;

机构地区： 太原理工大学数学学院,山西太原030024

出　　处： 《中北大学学报（自然科学版）》 2017年第4期404-408,共5页

摘　　要： 研究了一类二阶奇异摄动滞后型微分方程的边值问题.首先利用摄动方法中展开的思想对滞后项进行处理,将原系统转化为不含时滞项的近似系统.然后在一定的假设条件下,结合边界层位于t=1和t=0处这两种情形,利用奇异摄动方法和微分不等式技巧等对于方程的解给出了相应的存在性定理:在满足一定的条件下,对于足够小的ε>0,边值问题存在满足条件的解. The boundary value of a class of second-order singularly perturbed delaying differential equa- tion is studied. First, by using the polynomial expansion in the perturbation method to the delayed terms, the original system is transformed into an equivalent system without delayed terms. Then, under certain hypothetic conditions, different existing theorems can be given according to the positions of the boundary layers which is located at t=1 or t=0, through the singular perturbation method and the differential inequality technique. The theorem is. Under certain conditions, the boundary value has a solution to satisfy the condition if ε〉0 is small enough.

关 键 词： 二阶微分方程 奇异摄动 时滞 边界层 微分不等式