含有强迫项的高阶非线性中立型微分方程的振动性
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摘要
考虑了一类含有强迫项的高阶非线性中立型微分方程,通过运用Krasnoselskii′s不动点定理和分析技巧,得到了该方程每一个有界解振动或趋于零的充要条件.所得结果改进了一些已知结论,并给出了实例验证.
In this paper,we investigate a class of higher order nonlinear neutral differential equations with forced term.By using Krasnoselskii′s fixed point theorem and analytical technique,new necessary and sufficient conditions are obtained for every bounded solution which either oscillates or tends to zero.In particular,the obtained results improve some known results and two examples are given to show the applications of the results.
In this paper,we investigate a class of higher order nonlinear neutral differential equations with forced term.By using Krasnoselskii′s fixed point theorem and analytical technique,new necessary and sufficient conditions are obtained for every bounded solution which either oscillates or tends to zero.In particular,the obtained results improve some known results and two examples are given to show the applications of the results.
引文
[1]LADDE G S,LAKSHMIKANTHAM V,ZHANG B G.Oscillation theory of differential equations with deviating arguments[M].New York:Dekker,1987.
[2]AGARWAL RP,BOHNER M,LI W T.Nonoscillation and oscillation theorem for functional differential equations[M].New York:Dekker,2004.
[3]PARHI N.Oscillations of higher order differential equations of neutral type[J].Czech Math J,2000,50(1):155-173.DOI:10.1023/A:1022405707349.
[4]AGARWAL P R,GRACE S R.The oscillation of higher order differential equations with deviating arguments[J].Comput Math Appl,1999,38(3-4):185-199.DOI:10.1016/s0898-1221(99)00193-5.
[5]刘有俊,张建文,燕居让.带分布时滞高阶中立型微分方程非振动解的存在性[J].应用数学学报,2015,38(2):235-241.
[6]YILMAZ SAHINER Y,ZAFER A.Bounded oscillation of nonlinear neutral differential equations of arbitrary order[J].Czechoslovak Math J,2001,51(1):185-195.DOI:10.1023/A:1013763409361.
[7]CANDAN T,DAHIYA R S.Oscillation behavior of higher order neutral differential equations[J].Appl Math Comput,2005,167(2):1267-1280.DOI:10.1016/j.amc.2004.08.037.
[8]OU C H,WONG JAMES S W.Forced oscillation of nth-order functional differential equations[J].J Math Anal Appl,2001,262(2):722-732.DOI:10.1006/jmaa.2001.7614.
[9]DAHIYA R S,AKINYELE,OLUSOLA.Oscillation theorems of N th-order functional differential equations with forcing terms[J].J Math Anal Appl,1985,109(2):325-332.DOI:10.1016/0022-247X(85)90153-2.
[10]HAMEDANI G G.Oscillatory behavior of nth order forced functional differential equations[J].J Math Anal Appl,1995,195(1):123-134.DOI:10.1006/jmaa.1995.1346.
[11]林文贤.一类高阶中立型方程的强迫振动性[J].应用泛函分析学报,2007,9(2):117-120.
[12]ZHOU X L,YU RONG.Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients[J].Comput Math Appl,2008,56(6):1562-1568.DOI:10.1016/j.camwa.2008.03.006.
[13]BOLAT Y,AKIN O.Oscillatory behaviour of higher order neutral type nonlinear forced differential equations with oscillating coefficients[J].J Math Anal Appl,2004,290(1):302-309.DOI:10.1016/j.jmaa.2003.09.062.
[2]AGARWAL RP,BOHNER M,LI W T.Nonoscillation and oscillation theorem for functional differential equations[M].New York:Dekker,2004.
[3]PARHI N.Oscillations of higher order differential equations of neutral type[J].Czech Math J,2000,50(1):155-173.DOI:10.1023/A:1022405707349.
[4]AGARWAL P R,GRACE S R.The oscillation of higher order differential equations with deviating arguments[J].Comput Math Appl,1999,38(3-4):185-199.DOI:10.1016/s0898-1221(99)00193-5.
[5]刘有俊,张建文,燕居让.带分布时滞高阶中立型微分方程非振动解的存在性[J].应用数学学报,2015,38(2):235-241.
[6]YILMAZ SAHINER Y,ZAFER A.Bounded oscillation of nonlinear neutral differential equations of arbitrary order[J].Czechoslovak Math J,2001,51(1):185-195.DOI:10.1023/A:1013763409361.
[7]CANDAN T,DAHIYA R S.Oscillation behavior of higher order neutral differential equations[J].Appl Math Comput,2005,167(2):1267-1280.DOI:10.1016/j.amc.2004.08.037.
[8]OU C H,WONG JAMES S W.Forced oscillation of nth-order functional differential equations[J].J Math Anal Appl,2001,262(2):722-732.DOI:10.1006/jmaa.2001.7614.
[9]DAHIYA R S,AKINYELE,OLUSOLA.Oscillation theorems of N th-order functional differential equations with forcing terms[J].J Math Anal Appl,1985,109(2):325-332.DOI:10.1016/0022-247X(85)90153-2.
[10]HAMEDANI G G.Oscillatory behavior of nth order forced functional differential equations[J].J Math Anal Appl,1995,195(1):123-134.DOI:10.1006/jmaa.1995.1346.
[11]林文贤.一类高阶中立型方程的强迫振动性[J].应用泛函分析学报,2007,9(2):117-120.
[12]ZHOU X L,YU RONG.Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients[J].Comput Math Appl,2008,56(6):1562-1568.DOI:10.1016/j.camwa.2008.03.006.
[13]BOLAT Y,AKIN O.Oscillatory behaviour of higher order neutral type nonlinear forced differential equations with oscillating coefficients[J].J Math Anal Appl,2004,290(1):302-309.DOI:10.1016/j.jmaa.2003.09.062.