在线阅读 --自然科学版 2014年1期《时标上具有高阶导数的Opial型不等式》
时标上具有高阶导数的Opial型不等式--[在线阅读]
高志娟, 付旭扬
河北师范大学 数学与信息科学学院, 河北 石家庄 050024
起止页码: 14--18页
DOI: 10.11826/j.issn.1000-5854.2014.01.004
摘要
建立了时标上具有高阶导数的Opial型不等式,所得结论不仅推广了连续和离散下的相关结论,而且在时标上得到新的结果.

Opial-type Inequalities Involving Higher Order Delta Derivatives on Time Scales
GAO Zhijuan, FU Xuyang
College of Mathematics and Information Sciences, Hebei Normal University, Hebei Shijiazhuang 050024, China
Abstract:
In this paper, some new Opial-type inequalities involving higher order delta derivatives on time scales are established.These inequalities extend respective known results on the continuous and discrete case in the literature, and provide new estimates in the setting of time scales.

收稿日期: 2013-1-15
基金项目: 国家自然科学基金(11071054);河北省自然科学基金(A2011205012)

参考文献:
[1]AGARWAL R P,LAKSHMIKANTHAM V.Uniqueness and Nonuniqueness Criteria for Ordinary Dierential Equations [M].Singapore:World Scientic,1993.
[2]AGARWAL R P,PANG P Y H.Opial-type Inequalities Involving Higher Order Differences [J].Math Comput Model,1995,21:49-69.
[3]PACHPATTE B G.On Opial-type Integral Inequalities [J].Math Anal Appl,1986,120:547-556.
[4]OPIAL Z.Sur Une Inégalité [J].Ann Polon Math,1960,8:29-32.
[5]WILLETT D.The Existence-uniqueness Theorem for an Nth Order Iinear Ordinary Dierential Equation [J].Amer Math Monthly,1968,75:174-179.
[6]BEESACK P R,DAS K M.Extension of Opial's Inequality [J].Pacific Math,1968,26:215-232.
[7]ANASTASSIOU G A.Foundations of Nelba Fractional Calculus on Time Scales [J].Comput Math Appl,2010,59:3750-3762.
[8]CHEUNG W S,ZHAO D D,JOSIP P.Opial-type Inequalities for Dierential Operators [J].Nonlinear Anal,2007,66:2028-2039.
[9]CHEUNG W S.Some Generalized Opial-type Inequalities [J].Math Anal Appl,1991,162:317-321.
[10]ZHAO C J,CHEUNG W S.On Opial-type Inequalities with Higher Order Partial Derivatives [J].Appl Math Lett,2012,25:2156-2161.
[11]ANASTASSIOU G A.Opial Type Inequlities Involving Fractional Derivatives of Two Functions and Applications [J].Math Appl,2004,48:1701-1731.
[12]BOHNER M,PETERSON A.Dynamic Equations on Time Scales,An Introduction with Applications [M].Boston:Birkhäuser,2001.
[13]MARKS R J,DAVIS J M.A Generalized Fourier Transform and Convolution on Time Scales [J].Math Anal Appl,2008,340:901-919.