关于非线性退化时滞微分方程解的研究  

Investigation of a Nonlinear Degenerate Functional Differential Equation with Delay

作　　者：王健[1] 张志信[1] 蒋威[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《佳木斯大学学报（自然科学版）》2015年第4期630-633,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：国家自然科学基金(11371027;11071001);安徽省自然科学基金(KJ2013A032);教育部博士点基金(20123401120001);安徽大学本科生科研训练计划项目(J18520103);安徽大学博士科研启动经费(023033190142)

摘　　要：主要利用Gronwall不等式研究了一类非线性退化时滞微分方程解的存在性和解的指数估计问题.并对中立型的退化时滞微分方程,给出了将其转化为本文所研究的方程的具体方法,并推广了相关结论.最后通过例子验证了定理条件的存在性.By combining the integral inequality theorem of Gronwall,the existence and the exponential estimate of solution for a nonlinear degenerate functional differential equation with delay were considered. Neutral degenerate functional differential equation with delay can be converted into a nonlinear degenerate functional differential equation with delay by the method. The result obtained is the generalization of some results established before. An example was provided to illustrate the effectiveness of the presented analytical approaches.

关 键 词：非线性微分方程 退化 时滞 解的存在性 解的指数估计 

分 类 号：O175.9[理学—数学]