应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2005年
2期
293-296
,共4页
具连续变量差分方程%脉冲%振动
具連續變量差分方程%脈遲%振動
구련속변량차분방정%맥충%진동
Difference equation with continuous variable%Impluse%Oscillation
考虑新的一类具有连续变量的脉冲差分方程{x(t+τ-x(t)+p(t)x(t-rτ)=0, t≥to-τ,t≠tk, x(tk+τ)gx(tk)=bkx(tk), t∈ N(1),其中p(t)是[t0-τ,∞]上的非负连续函数,τ＞0,bk是常数,r是正整数,0≤t0＜t1＜t2＜…＜tk＜…且limtkk→∞=∞,获得了方程所有解振动的充分条件.
攷慮新的一類具有連續變量的脈遲差分方程{x(t+τ-x(t)+p(t)x(t-rτ)=0, t≥to-τ,t≠tk, x(tk+τ)gx(tk)=bkx(tk), t∈ N(1),其中p(t)是[t0-τ,∞]上的非負連續函數,τ＞0,bk是常數,r是正整數,0≤t0＜t1＜t2＜…＜tk＜…且limtkk→∞=∞,穫得瞭方程所有解振動的充分條件.
고필신적일류구유련속변량적맥충차분방정{x(t+τ-x(t)+p(t)x(t-rτ)=0, t≥to-τ,t≠tk, x(tk+τ)gx(tk)=bkx(tk), t∈ N(1),기중p(t)시[t0-τ,∞]상적비부련속함수,τ＞0,bk시상수,r시정정수,0≤t0＜t1＜t2＜…＜tk＜…차limtkk→∞=∞,획득료방정소유해진동적충분조건.
We obtian sufficient conditions for osillation of all solutions of the impulsive difference equation with continuous variable{x(t+τ-x(t)+p(t)x(t-rτ)=0, t≥to-τ,t≠tk, x(tk+τ)-x(tk)=bkx(tk), t∈ N(1),where p(t)≥0 is continuous on [t0 -τ,∞],τ＞ 0,bk are constants, r is a positive integer, 0 ≤ t0<t1<t2<…<tk<…with limtkk→∞=∞.
