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Gronwall积分不等式在微分方程中的应用 被引量:5

THE APPLICATION OF INTEGRAL INEQUATION IN A DIFFERENTIAL EQUATION
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摘要  引用Gronwall积分不等式建立了函数矩阵中的一个Gronwall型积分不等式,并由此证明了一阶微分方程及一类函数矩阵微分方程解的唯一性. The article cites Gronwall integral inequation and erects a Gronwall integral inequation in function matrix. Thereout it proves the result of one-level differential equation and function matrix equation is unique.
出处 《佳木斯大学学报(自然科学版)》 CAS 2004年第3期417-419,共3页 Journal of Jiamusi University:Natural Science Edition
关键词 Gronwall积分不等式 微分方程 唯一性 Gronwall type inquality integral equality uniqueness
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参考文献2

  • 1东北师大数学系.常微分方程[M].北京:高等教育出版社,1982..
  • 2王高雄.常微分方程[M].北京:高等教育出版社,2001..

共引文献15

同被引文献28

  • 1魏章志,梅宇,陈浩.Gronwall不等式及其应用[J].宿州师专学报,2003,18(3):65-66. 被引量:3
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  • 4A. A. Kilbas, H. M. Sfivastava, J. J. TrujiUo. Theory and ap- plications of fractional differential equations [ M ]. Elsevier Sci- ence B. V. , Amsterdam, The Netherlands, 2006.
  • 5Podlubny. Fractional differential equation [ M ]. San Diego:Aca- demic Press , 1999.
  • 6H. Ye,J. Gao,Y. Ding. A generalized Gronwall inequality and its application to a fractional differential equation [ J ]. Journal of Mathematical Analysis and Applications,2007,328 ( 2 ) : 1075 - 1081.
  • 7K. S. Miller, B. Ross. An introduction to the fractional calculus and fractional differential equations[ J]. John Wiley & Sons, NewYork, NY, USA, 1993.
  • 8K. Diethelm. The analysis of fractional differential equations [J]. Springer, Berlin , Germany, 2010.
  • 9M. P. Lazarevi'c, A. M. Spasi'c. Finite-time stability analy- sis of fractional order time - delay systems: Gronwall' s approach [J]. Mathematical and Computer Modelling, 2009 , 49(3 -4) : 475 - 481.
  • 10Ahdulaziz Aloft , Jinde Cao , Ahmed Elaiw, Abdullab A1- Mazrooeil. Delay - dependent stability criterion of Caputo frac- tional neural networks with distributed delay[J ]. Discrete Dynam- ics in Nature and Society,2014 ,Article ID 529358:1 -6.

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