一阶泛函微分方程变号周期解的存在性  

On Sign-changing Periodic Solutions for First Order Functional Differential Equations

作　　者：康淑瑰[1] 

机构地区：[1]山西大同大学数学与计算机科学学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2014年第1期1-3,7,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西大同大学博士科研启动基金项目[2010-B-01];国家自然科学基金项目[11271235]

摘　　要：利用不动点理论,讨论如下方程y′(t)=-a(t)y(t)+f(t,y(t-τ(t)))变号周期解的存在性,给出方程三个非零变号周期解的存在性,其中一个是正的,一个是负的,另一个是变号的。In this paper, the existence of sign-changing periodic solutions for first order functional differential equations of the form y（t）=-a（t）y（t）＋f（t,y（t-τ（t））） is considered by using the fixed point theorems. The main results are some new three-solution theorem, which are different from the results in [3,4]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution.

关 键 词：一阶泛函微分方程 锥 e-连续 变号周期解 不动点定理 

分 类 号：O175.7[理学—数学]