一类有偏差变元的泛函微分方程的2π周期解  

PERIODIC SOLUTION FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH PARTIAL DIFFERENCE VARIABLES

作　　者：林壮鹏[1] 徐远通[2] 郭志明[2] 

机构地区：[1]深圳大学理学院数学系,广东深圳518060 [2]中山大学数学系,广东广州510275

出　　处：《高校应用数学学报（A辑）》2000年第4期421-427,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：用迭合度理论研究一类有偏差变元的泛函微分方程 x″(t) +f(x(t) ) x′(t) + bx(t) + g(x(t-τ1 (t,x(t) ,x′(t) ) ) ,… ,x(t-τm(t,x(t) ,x′(t) ) ) ) =p(t)的 2π周期解的存在性 ,从本质上改进和推广了张正球等人 (1 998年 )的相应结果 .In this paper,the theory of coincidence degree is used to study the existence of the periodic solutions for a class of functional differential equations with partial difference variables x″(t)+f(x(t))x′(t)+bx(t)+g(x(t-τ\-1(t,x(t),x′(t))),…, x(t-τ\-m(t,x(t),x′(t))))=p(t) and a new result is obtained,which is the essential improvement of the theorem in the previous papers.

关 键 词：偏差变元 泛函数分方程 周期解 迭合度 DUFFING方程 

分 类 号：O175.14[理学—数学]