一类高阶非线性时滞微分方程解的振动性
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摘要
研究一类高阶非线性时滞微分方程解的振动性,借助Riccati变换、Kigundgze引理对非线性项和高阶项进行处理,从而达到线性化和降阶的目的,并利用Philos的积分平均方法,建立这类方程解的振动准则,给出了方程解振动的若干充分条件,推广和包含已有文献的结论.
Oscillation for solutions of certain higher order nonlinear delays differential equation.Riccati transformation and Kiguradgze Lemma are used here to change the nonlinear terms to linear ones and higher order terms into lower order terms.By using Philo s integral average method,some sufficient conditions of oscillation are advanced;oscillation criteria of solutions of the equations are established,which generalize and improve some known results.
Oscillation for solutions of certain higher order nonlinear delays differential equation.Riccati transformation and Kiguradgze Lemma are used here to change the nonlinear terms to linear ones and higher order terms into lower order terms.By using Philo s integral average method,some sufficient conditions of oscillation are advanced;oscillation criteria of solutions of the equations are established,which generalize and improve some known results.
引文
[1]朱刚.任洪善,俞元洪.高阶非线性时滞微分方程解的振动性[J].黑龙江大学自然科学学抿2008,25(2):264-266.
[2]YURIVR.Oscillationcriteriaforcertainnonlinear differential equations[J].Journal of Mathematics Analysis and Applications,1992(29):399-416.
[3]GRACE S R.Oscillation theorems for nonlinear differential equations of second order[J].J Math.Anal.Appl,1992(71):220-241.
[4]YURI V R.Oscillation of a second order nonlinear delay differential equations[J].Funkcialaj Ekvacioj,2000,43(1):1-29.
[5]KIGURADZEIT.On the oscillation of some ordinary diffe-rential equations[J].Dokl Akad Nauk SSSR.1962(144)33-36.
[6]PHILOS C G.A new criterion for the oscillatory and asymptotic behavior of delay differential equations[J].Bull AcadPolSciSerSciMat,1981(39):61-64.
[2]YURIVR.Oscillationcriteriaforcertainnonlinear differential equations[J].Journal of Mathematics Analysis and Applications,1992(29):399-416.
[3]GRACE S R.Oscillation theorems for nonlinear differential equations of second order[J].J Math.Anal.Appl,1992(71):220-241.
[4]YURI V R.Oscillation of a second order nonlinear delay differential equations[J].Funkcialaj Ekvacioj,2000,43(1):1-29.
[5]KIGURADZEIT.On the oscillation of some ordinary diffe-rential equations[J].Dokl Akad Nauk SSSR.1962(144)33-36.
[6]PHILOS C G.A new criterion for the oscillatory and asymptotic behavior of delay differential equations[J].Bull AcadPolSciSerSciMat,1981(39):61-64.