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Gronwall积分不等式的推广 被引量:3

Generalization of Gronwall Integral Inequalities
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摘要 将一维函数的Gronwall不等式推广到了n维欧几里得空间. In this paper the authors generalize 1-independent-variable the integral inequalities by Gronwall and establish the integral inequalities in the n-dimensional Euclidean space Rn.
出处 《西南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2005年第4期760-762,共3页 Journal of Southwest China Normal University(Natural Science Edition)
关键词 连续函数 GRONWALL不等式 欧几里得空间 continuous function generalization of Gronwall integral inequalities Euclidean space
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参考文献2

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  • 2王高雄 周之铭 朱思铭 等.常微分方程[M].北京:高等教育出版社,1978.65-79.

共引文献42

同被引文献21

  • 1钟五一,杨必成.关于反向Hardy-Hilbert积分不等式的推广[J].西南大学学报(自然科学版),2007,29(4):44-48. 被引量:16
  • 2Bellman R. The Stability of Solutions of Linear Differential Equations [J]. Duke Math J, 1943, 10:643 -647.
  • 3Gronwall T H. Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations [J]. Ann Math, 1919, 20: 292--296.
  • 4Zhang W, Deng S. Projected Gronwall-Bellman's Inequality for Integrable Functions [J]. Math Comput Modelling, 2001, 34:394 -- 402.
  • 5Cheung W S. Some New Nonlinear Inequalities and Applications to Boundary Value Problems [J]. Nonlinear Anal, 2006, 64: 2112--2128.
  • 6Wang W S. A Generalized Retarded Gronwall like Inequality in two Variables and Applications to BVP [J]. Appl Math Comput, 2007, 191(1): 144--154.
  • 7Agarwal R P, Deng S, Zhang W. Generalization of a Retarded Gronwall like Inequality and its Applications [J]. Appl Math Comput, 2005, 165:599--612.
  • 8Kim Y H. Gronwall, Bellman and Pachpatte Type Integral Inequalities with Applications [J]. Nonlinear Anal, 2009, 71: 2641 -- 2656.
  • 9Cheung W S, Ren J. Discrete Non-linear Inequalities and Applications to Boundary Value Problems [J]. J Math Anal Appl, 2006, 319:708--724.
  • 10Ma Q H, Cheung W S. Some New Nonlinear Difference Inequalities and Their Applications [J]. J Comput Appl Math, 2007, 202:339 -- 351.

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