带强迫项的高阶中立型方程非振动解的渐近性  

Asymptotic Behavior of Nonoscillatory Solutions for Forced High Order Neutral Differential Equation

作　　者：宋淑红[1] 闫智勇[2] 

机构地区：[1]山西大学数学系,山西太原030006 [2]华北水利水电学院,河北邯郸056021

出　　处：《山西大学学报（自然科学版）》2002年第4期285-288,共4页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金 (2 0 0 0 10 0 1)

摘　　要：文章得到带有强迫项的中立型高阶微分方程(x(t) - p(t) x(t-τ) ) ( n) +Q(t) G(x(t-σ) ) =f (t)在条件(i) G∈ C(R,R) ,x G(x) >0 (x≠ 0 ) ,且 G是不减的 ;(ii)τ≥ 0 ,σ≥ 0 ,Q∈ C([0 ,∞ ) ,[0 ,∞ ) ) ,p∈ C([0 ,∞ ) ,R) ,且 0≤ p(t)≤ p1 <1;(iii) f∈ C([0 ,∞ ) ,R)且存在 F∈ Cn([0 ,∞ ) ,R)使得 F( n) (t) =f(t) ,limt→∞F(t) =M∈ R存在下所有非振动解当 t→∞时趋于零的充分条件和必要条件分别为∫∞0Q(t) dt=∞和∫∞0sn- 1 Q(s) ds=∞ .Based on the following hypotheses (i) G∈C(R,R),xG(x)>0 for x≠0, and G is non decreasing; (ii) τ≥0,σ≥0,Q,p∈C([0,∞),[0,∞)), and 0≤p(t)≤p\-1<1; (iii) f∈C([0,∞),R) and exists F∈C\+n([0,∞),R), such that F\+\{(n)\}(t)=f(t), \{lim\} [DD(X]t→∞F(t)=M∈R exists,sufficient condition and necessary condition∫\+∞\-0Q(t) d t=∞ and ∫\+∞\-0s\+\{n-1\}Q(s) d s=∞are obtained,ensuring that every non oscillatory solution of the high order neutral differential equation(x(t)-p(t)x(t-τ))\+\{(n)\}+Q(t)G(x(t-σ))=f(t)tends to zero as t→∞.

关 键 词：高阶中立型方程 强迫项 非振动解 渐近性 充要条件 

分 类 号：O175.1[理学—数学] O241.81[理学—基础数学]