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一类新型具有两个独立变量的不连续函数的积分不等式 被引量：2

SOME NEW INTEGRAL INEQUALITIES FOR DISCONTINUOUS FUNCTION OF TWO INDEPENDENT VARIABLES
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摘要 主要研究了具有两个独立变量的不连续函数(有跳跃间断点)的一类更为广泛的新型积分不等式(Wendroff型),得出了一些新的结论,从而推广了前人的工作. In this article, some new integral inequalities of discontinuous function in two independent variables is investigated, some new results are obtained, which generalize some existing conclusions.
作者 孟东沅 孟凡伟
机构地区 青岛理工大学理学院 曲阜师范大学数学系
出处 《系统科学与数学》 CSCD 北大核心 2009年第4期440-450,共11页 Journal of Systems Science and Mathematical Sciences
关键词 积分不等式 不连续函数 独立变量 Wendroff型 Integral inequality, discontinuous function.
分类号 O178 [理学—基础数学] O174.41 [理学—基础数学]
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参考文献8

  • 1Snow D R. Gronwall's inequality for systems of partial differential equations in two independent variable. Proc. Amer. Math. Soc., 1972, 33: 46-54.
  • 2Borysenko S D. Integro-sum inequalities for functions of many independent variables. Differ. Equ., 1989, 25(9): 1634-1641.
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  • 4Borysenko D S. About one integral inequality for piece-wise continuous functions. Proceedings of the International Kravchuk Conference, Kyiv, 2004.
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  • 6Sergiy Borysenko, Gerardo Iovane. About some new integral inequalities of wendroff type for discontinuous functions. Nonlinear Analysis, 2007, 66: 2190-2203.
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  • 8Gallo A, Piccirillo A M. About new analogies of Gronwall-Bellman-Bihari type inequalities for discontinuous and estimated solutions for impulsive differential systems. Nonlinear Analysis, 2007, 67: 1551-1559.

同被引文献32

  • 1Bellman R.The stability of solutions of linear differential equations[J].Duke Math J,1943,10:643-647.
  • 2Zhang W,Deng S.Projected Gronwall-Bellman’s inequality for integrable functions[J].Math Comput Model,2001,34:394-402.
  • 3Wang W S.A generalized retarded Gronwall-like inequality in two variables and applications to BVP[J].Appl Math Comput,2007,191(1):144-154.
  • 4Wang W S.Estimation on certain nonlinear discrete inequality and applications to boundary value problem[J].Adv DifferenceEqns,2009,2009:708587.
  • 5Choi S K,Deng S,Koo N J,et al.Nonlinear integral inequalities of Bihari-Type without class H[J].Math Inequ Appl,2005,8(4):643-654.
  • 6Xu R,Sun Y G.On retarded integral inequalities in two independent variables and their applications[J].Appl Math Comput,2006,182:1260-1266.
  • 7Kim Y H.Gronwall,Bellman and Pachpatte type integral inequalities with applications[J].Nonl Anal,2009,71:2641-2656.
  • 8Lipovan O.A retarded Gronwall-like inequality and its applications[J].J Math Anal Appl,2000,252:389-401.
  • 9Agarwal R P,Deng S,Zhang W.Generalization of a retarded Gronwall-like inequality and its applications[J].Appl MathComput,2005,165:599-612.
  • 10Agarwal R P,Kim Y H,Sen S K.New retarded integral inequalities with applications[J].J Inequ Appl,2008,2008:908784.

引证文献2

二级引证文献10

系统科学与数学
2009年 第4期

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