一类高阶中立型微分方程的正周期解  

Positive Periodic Solutions for a Kind of Higher-Order Neutral Differential Equations

作　　者：赵明睿 李永祥[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2016年第2期246-250,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11261053);甘肃省自然科学基金(批准号:1208RJZA129)

摘　　要：用全连续算子与压缩算子和的Krasnoselskii不动点定理研究高阶中立型时滞微分方程d^n/dt^n(u(t)-cu(t-δ))+M(u(t)-cu(t-δ))=f(t,u(t-τ_1),…,u(t-τ_m))正2π-周期解的存在性,其中:δ>0;0<c<1;M>0为常数;f:R×[0,∞)~m→[0,∞)连续,关于t以2π为周期;τ_1,τ_2,…,τm≥0为常数,获得了该方程正周期解的存在性与多重性结果.Applying the Krasnoselskii＇s fixed point theorem of the sum of a completely continuous operator and a contractive operator,we discussed the existence of positive 2π-periodic solutions for the higher-order neutral differential equationdn d^n/dt^n（u（t）-cu（t-δ））＋M（u（t）-cu（t-δ））=f（t,u（t-τ_1）,…,u（t-τ_m））where δ0,0c1,and M0 are constants,f： R×[0,∞）m→[0,∞） is a continuous function which is 2π-periodic for t and τ_1,τ_2,…,τm≥ 0 are constants. Existence and multiplicity results of positive periodic solutions were obtained for the equation.

关 键 词：中立型微分方程 正周期解 全连续算子 压缩算子 KRASNOSELSKII不动点定理 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]