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一个新的非线性差分不等式及其应用 被引量：2

A NEW NONLINEAR DIFFERENCE INEQUALITY AND ITS APPLICATION
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摘要 建立了一个一般形式的二变量的差分不等式,该不等式和号内包含两个不同的没有假设单调性的未知函数的复合函数,使用了单调化技术,利用了强单调的性质,给出了未知函数的估计,结果能对Ma Q H等人文中考虑的离散不等式的未知函数进行估计,进一步,给出了差分方程解的估计。 In this paper a general form of difference inequality in two variables is established, which includes both two distinct nonlinear composite functions of unknown function in the sums without an assumption of monotonicity. In terms of the monotonization technique and by using the monotonicity, an estimate for the unknown function is given. The result can be used to solve those discrete inequalities considered by Ma. Finally, the result is applied to give estimation of solutions of a difference equation.
作者 王五生
机构地区 河池学院数学系
出处 《系统科学与数学》 CSCD 北大核心 2009年第12期1664-1671,共8页 Journal of Systems Science and Mathematical Sciences
基金 广西自然科学基金项目(200991265) 广西教育厅科学研究项目(200707MS112) 广西新世纪教改工程"十一五"第三批资助项目(200710961) 河池学院应用数学重点学科(200725)
关键词 差分不等式 差分方程 解的估计. Difference inequality, difference equation, estimation of solutions.
分类号 O175.7 [理学—基础数学]
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参考文献18

  • 1Bellman R. The stability of solutions of linear differential equations. Duke Math. J., 1943, 10: 643-647.
  • 2Gronwall T H. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. of Math., 1919, 20: 292-296.
  • 3Bainov D and Simeonov P. Integral Inequalities and Applications. Dordrecht, Kluwer Academic, 1992.
  • 4Mitrinovic D S, Pecaric J E and Fink A M. Inequalities Involving Functions and Their Integrals and Derivatives. Dordrecht, Kluwer Academic, 1991.
  • 5Pachpatte B G. Inequalities for Differential and Integral Equations. New York, Academic Press, 1998.
  • 6Agarwal R P, Deng S and Zhang W. Generalization of a retarded Gronwall-like inequality and its applications. Appl. Math. Comput., 2005, 165, 599412.
  • 7Lipovan O. Integral inequalities for retarded Volterra equations. J. Math. Anal. Appl., 2006, 322: 349-358.
  • 8Ma Q M and Yang E H. On some new nonlinear delay integral inequalities. J. Math. Anal. Appl., 2006, 252: 864- 878.
  • 9Zhang W and Deng S. Projected Gronwall-Bellman's inequality for integrable functions. Math. Comput. Modelling, 2001, 34:394-402.
  • 10Wang W S. A generalized retarded Gronwall-like inequality in two variables and applications to BVP. Appl. Math. Comput., 2007, 191:144-154.

同被引文献13

  • 1周玛莉,吴行平.Gronwall积分不等式的推广[J].西南师范大学学报（自然科学版）,2005,30(4):760-762. 被引量：3
  • 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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二级引证文献7

系统科学与数学
2009年 第12期

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