一类三阶非线性分布时滞动力方程的振动结果
|
摘要
研究一类三阶非线性分布时滞动力方程的振动性,通过构造广义Riccati变换得到一类新的广义Riccati不等式,利用积分平均技巧等方法,建立了保证该方程一切解均振动或收敛于0的若干新的振动结果,推广和改进了近期文献的相关结论,并给出了若干例子。
In the paper, oscillatory behaviors for a class of the third order nonlinear dynamic equations with distributed delays are studied. Using methods such as generalized Riccati transformation and Integral averaging technique, some new sufficient criteria are established that any solution of the equations will be either oscillatory or convergent to zero.The results extend the respective studies in recent literature, and give a number of examples to prove the efficiency.
In the paper, oscillatory behaviors for a class of the third order nonlinear dynamic equations with distributed delays are studied. Using methods such as generalized Riccati transformation and Integral averaging technique, some new sufficient criteria are established that any solution of the equations will be either oscillatory or convergent to zero.The results extend the respective studies in recent literature, and give a number of examples to prove the efficiency.
引文
[1]PHILOS C G.On a Kamenev’s integral criterion for oscillation of linear differential equations of second order[J].Annals Polonais Mathematics,1983,21:175-194.
[2]PHILOS C G.Oscillation theorems for linear differential equations of second order[J].Archiv Der Mathematik,1989,53(5):482-492.
[3]SUN Y G,MENG F W.Note on the paper of Dzurina and Stavroulakis[J].Applied Mathematics and Computation,2006,174(2):1634-1641.
[4]BACULíKOVáB,LI T X,D?URINA J.Oscillation theorems for second-order superlinear neutral differential equations[J].Mathematica Slovaca,2013,63(1):123-134.
[5]LIU H D,FAN W M,LIU P C.Oscillation and asymptotic analysis on a new generalized EmdenFowler equation[J].Applied Mathematics and Computation,2012,219(5):2739-2748.
[6]AGARWAL R P,BOHNER M,LI T X,et al.Oscillation of second-order Emden-Fowler neutral delay differential equations[J].Annali di Matematica Pura ed Applicata,2014,193(6):1861-1875.
[7]WU Y Z,YU Y H,ZHANG J M,et al.Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type[J].Journal of Inequalities and Applications,2016,2016(1):328-338.
[8]黄记洲,符策红.广义Emden-Fowler方程的振动性[J].应用数学学报,2015,38(6):1126-1135.HUANG J Z,FU C H.Oscillation criteria of generalized Emden-Fowler equations[J].Acta Mathematicae Applicatae Sinica,2015,38(6):1126-1135.
[9]杨甲山,覃桂茳.一类二阶微分方程新的Kamenev型振动准则[J].浙江大学学报(理学版),2017,44(3):274-280.YANG J S,QIN G J.Kamenev-type oscillation criteria for certain second-order differential equations[J].Journal of Zhejiang University(Science Edition),2017,44(3):274-280.
[10]BACULíKOVáB,D?URINA J.Oscillation of thirdorder neutral differential equations[J].Mathematical and Computer Modelling,2010,52(1):215-226.
[11]THANDAPANI E,LI T X.On the oscillation of third-order quasi-linear neutral functional differential equations[J].Archivum Mathematicum,2011,47(3):181-199.
[12]LI T X,ZHANG C H.Properties of third-order halflinear dynamic equations with an unbounded neutral coefficient[J].Advances in Difference Equations,2013,2013(1):1-8.
[13]JIANG Y,LI T X.Asymptotic behavior of a thirdorder nonlinear neutral delay differential equation[J].Journal of Inequalities and Applications,2014,2014(1):512.
[14]YANG L L,XU Z T.Oscillation of certain thirdorder quasilinear neutral differential equation[J].Mathematica Slovaca,2014,64(1):85-100.
[15]JIANG Y,JIANG C M,LI T X.Oscillatory behavior of third-order nonlinear neutral delay differential equations[J].Advances in Difference Equations,2016,2016(1):171.
[16]YANG X J.Oscillation criterion for a class of quasilinear differential equations[J].Applied Mathematics and Computation,2004,153(1):225-229.
[2]PHILOS C G.Oscillation theorems for linear differential equations of second order[J].Archiv Der Mathematik,1989,53(5):482-492.
[3]SUN Y G,MENG F W.Note on the paper of Dzurina and Stavroulakis[J].Applied Mathematics and Computation,2006,174(2):1634-1641.
[4]BACULíKOVáB,LI T X,D?URINA J.Oscillation theorems for second-order superlinear neutral differential equations[J].Mathematica Slovaca,2013,63(1):123-134.
[5]LIU H D,FAN W M,LIU P C.Oscillation and asymptotic analysis on a new generalized EmdenFowler equation[J].Applied Mathematics and Computation,2012,219(5):2739-2748.
[6]AGARWAL R P,BOHNER M,LI T X,et al.Oscillation of second-order Emden-Fowler neutral delay differential equations[J].Annali di Matematica Pura ed Applicata,2014,193(6):1861-1875.
[7]WU Y Z,YU Y H,ZHANG J M,et al.Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type[J].Journal of Inequalities and Applications,2016,2016(1):328-338.
[8]黄记洲,符策红.广义Emden-Fowler方程的振动性[J].应用数学学报,2015,38(6):1126-1135.HUANG J Z,FU C H.Oscillation criteria of generalized Emden-Fowler equations[J].Acta Mathematicae Applicatae Sinica,2015,38(6):1126-1135.
[9]杨甲山,覃桂茳.一类二阶微分方程新的Kamenev型振动准则[J].浙江大学学报(理学版),2017,44(3):274-280.YANG J S,QIN G J.Kamenev-type oscillation criteria for certain second-order differential equations[J].Journal of Zhejiang University(Science Edition),2017,44(3):274-280.
[10]BACULíKOVáB,D?URINA J.Oscillation of thirdorder neutral differential equations[J].Mathematical and Computer Modelling,2010,52(1):215-226.
[11]THANDAPANI E,LI T X.On the oscillation of third-order quasi-linear neutral functional differential equations[J].Archivum Mathematicum,2011,47(3):181-199.
[12]LI T X,ZHANG C H.Properties of third-order halflinear dynamic equations with an unbounded neutral coefficient[J].Advances in Difference Equations,2013,2013(1):1-8.
[13]JIANG Y,LI T X.Asymptotic behavior of a thirdorder nonlinear neutral delay differential equation[J].Journal of Inequalities and Applications,2014,2014(1):512.
[14]YANG L L,XU Z T.Oscillation of certain thirdorder quasilinear neutral differential equation[J].Mathematica Slovaca,2014,64(1):85-100.
[15]JIANG Y,JIANG C M,LI T X.Oscillatory behavior of third-order nonlinear neutral delay differential equations[J].Advances in Difference Equations,2016,2016(1):171.
[16]YANG X J.Oscillation criterion for a class of quasilinear differential equations[J].Applied Mathematics and Computation,2004,153(1):225-229.