時(shí)標(biāo)上帶強(qiáng)迫項(xiàng)高階中立型動(dòng)力方程的振動(dòng)性與非振動(dòng)解的存在性

楊軍,劉帥,侯小康

(1.燕山大學(xué)理學(xué)院,河北秦皇島 066004;2.河北省數(shù)學(xué)研究中心,河北石家莊 050000)

時(shí)標(biāo)上帶強(qiáng)迫項(xiàng)高階中立型動(dòng)力方程的振動(dòng)性與非振動(dòng)解的存在性

楊軍1,2,劉帥1,侯小康1

(1.燕山大學(xué)理學(xué)院,河北秦皇島 066004;2.河北省數(shù)學(xué)研究中心,河北石家莊 050000)

給出時(shí)標(biāo)上一類帶強(qiáng)迫項(xiàng)高階中立型動(dòng)力方程一切解振動(dòng)和非振動(dòng)解存在的若干充分條件.所得結(jié)果推廣了一些已有的結(jié)論.

時(shí)標(biāo);動(dòng)力方程;強(qiáng)迫項(xiàng);振動(dòng)性;存在性

1 方程描述及定義

在微分、差分領(lǐng)域具有強(qiáng)迫項(xiàng)的方程已有一些研究成果[14],本文考慮時(shí)標(biāo)T上一類帶強(qiáng)迫項(xiàng)非線性高階中立型變時(shí)滯動(dòng)力方程

2 主要結(jié)果

[1]楊軍,關(guān)新平,劉樹堂.具強(qiáng)迫項(xiàng)高階非線性中立型差分方程的振動(dòng)性與漸近性[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué), 1999,15(4):29-35.

[2]曹賢通,皮上超,俞元洪.帶強(qiáng)迫項(xiàng)高階中立型微分方程的振動(dòng)性和非振動(dòng)性[J].數(shù)學(xué)的實(shí)踐與認(rèn)識, 2007,37(18):201-204.

[3]Parhin,Ratn R N.Oscillation criteria for forced first order neutra1 differential equations with variable coefficients[J].J.Math.Anal.Appl.,2001,256(2):525-541.

[4]Zhang Q X,Yan J R.Oscillation behavior of even order neutral differential equations with variable coefficients[J].Appl.Math.Letters,2006,19(11):1202-1206.

[5]Bohner M,Peterson A.Dynamic Equations on Time Scales:An Introduction with Applications[M].Boston: Birkh¨auser,2001.

Oscillation and existence of nonoscillatory solutions of forced higher order neutral dynamic systems on time scales

YANG Jun1,2,LIU Shuai1,HOU Xiao-kang1

(1.College of Sciences,Yanshan University,Qinhuangdao066004,China;
2.Mathematics Research Center in Hebei Province,Shijiazhuang050000,China)

Sufficient conditions are obtained for oscillation and existence of nonoscillatory solutions of a class of forced higher order neutral dynamic systems on time scales.The criteria generalize some known results.

time scales,dynamic systems,forced,oscillation,existence

O175.15

A

1008-5513(2009)04-0665-06

2008-07-08.

國家自然科學(xué)基金(60604004),河北省自然科學(xué)基金數(shù)學(xué)研究專項(xiàng)資助項(xiàng)目(07M005).

楊軍(1964-),博士,教授,研究方向：微分方程理論及應(yīng)用.

2000MSC:34K11,34C11,39A11