关于一类具偏差变元的Duffing型方程的周期解注记
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摘要
利用重合度理论以及更精确的先验估计研究了一类具有偏差变元的Duffing型方程的周期解问题,得到了这类方程的周期解存在性的结果,改进和推广了已有文献的相关结果,并给出其应用实例.
By coincidence degree’s theory and better prior estimate,the existence of periodic solutions to a kind of Duffing equation with deviating arguments is studied.Some new results on the existence of periodic solutions to such equation are obtained,which improve some existing ones in the literature.An example is given.
By coincidence degree’s theory and better prior estimate,the existence of periodic solutions to a kind of Duffing equation with deviating arguments is studied.Some new results on the existence of periodic solutions to such equation are obtained,which improve some existing ones in the literature.An example is given.
引文
[1]弭鲁芳,武延树,张萍萍.一类具时滞耗散型Duffing方程的周期解[J].数学的实践与认识,2008,38(19):235-238.
[2]黄记洲.一类时滞Duffing方程周期存在性的充分性定理[J].甘肃联合大学学报:自然科学版,2006,20(6):29-31.
[3]沈钦锐,周宗福.一类三阶时滞Duffing型方程周期解的存在唯一性[J].集美大学学报:自然科学版,2012,17(2):142-146.
[4]Li Xiaojiang,Zhou Youming,Chen Xuangqing,et al.On the ex-istence and uniqueness of periodic solution for Duffing type dif-ferential equations with a deviating argument[J].MathematicaApplicata,2012,25(2):335-340.
[5]刘怡建,陈晓星.一类带时滞的Duffing方程概周期解的存在性[J].福州大学学报:自然科学版,2011,39(3):329-333.
[6]李潇寰,蒋振.一类中立型Duffing方程的周期解[J].宝鸡文理学院:自然科学版,2011,31(3):10-12.
[7]张正球,庚建设.一类时滞Duffing型方程的周期解[J].高校应用数学学报:A辑,1998,13(4):389-392.
[8]肖兵,周启元.一类具偏差变元的Duffing型方程的周期解[J].江西师范大学学报:自然科学版,2007,31(1):29-33.
[9]Gaines R E,Mawhin J L.Lecture notes in math[M].Berlin:Springer-Verlag,1977.
[10]黄先开,向子贵.具有时滞的Duffing型方程x″+g(x(tτ(t)))=p(t)的2π周期解[J].科学通报,1994,39(3):201-203.
[2]黄记洲.一类时滞Duffing方程周期存在性的充分性定理[J].甘肃联合大学学报:自然科学版,2006,20(6):29-31.
[3]沈钦锐,周宗福.一类三阶时滞Duffing型方程周期解的存在唯一性[J].集美大学学报:自然科学版,2012,17(2):142-146.
[4]Li Xiaojiang,Zhou Youming,Chen Xuangqing,et al.On the ex-istence and uniqueness of periodic solution for Duffing type dif-ferential equations with a deviating argument[J].MathematicaApplicata,2012,25(2):335-340.
[5]刘怡建,陈晓星.一类带时滞的Duffing方程概周期解的存在性[J].福州大学学报:自然科学版,2011,39(3):329-333.
[6]李潇寰,蒋振.一类中立型Duffing方程的周期解[J].宝鸡文理学院:自然科学版,2011,31(3):10-12.
[7]张正球,庚建设.一类时滞Duffing型方程的周期解[J].高校应用数学学报:A辑,1998,13(4):389-392.
[8]肖兵,周启元.一类具偏差变元的Duffing型方程的周期解[J].江西师范大学学报:自然科学版,2007,31(1):29-33.
[9]Gaines R E,Mawhin J L.Lecture notes in math[M].Berlin:Springer-Verlag,1977.
[10]黄先开,向子贵.具有时滞的Duffing型方程x″+g(x(tτ(t)))=p(t)的2π周期解[J].科学通报,1994,39(3):201-203.