一类非局部时滞微分方程的上下解

Upper-lower solutions of nonlocal delayed differential equations

考虑非局部时滞微分方程cφ′(ξ)=∫RJ(ξ-y)φ(y)dy-φ(ξ)+f(φ(ξ),φ(ξ-cτ)),利用泰勒公式以及一些数学分析方法,给出了其上下解存在的充分条件以及具体的上下解,并用实例验证了本文结果的可行性.本文结果推广了文献[1]中的相应结果.

Using Taylor＇s formula and some analysis methods,we consider the following nonlocal delayed differential equation cφ′（ξ）=∫RJ（ξ-y）φ（y）dy-φ（ξ）＋f（φ（ξ）,φ（ξ-c τ））,and obtain the sufficient conditions to ensure the existence of upper-lower solutions.The specific upper-lower solutions are given.The feasibility of our results is illustrated by one example.The results in this paper generalize the corresponding results in reference [1].