| 二元积分不等式的若干推广及应用 |
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| 引用本文： | 曾冰,钟吉玉,段樱桃.二元积分不等式的若干推广及应用[J].四川大学学报(自然科学版),2016,53(2):280-288. |
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| 作者姓名： | 曾冰 钟吉玉 段樱桃 |
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| 作者单位： | 岭南师范学院 |
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| 基金项目： | 国家自然科学基金(11371314)和广东省自然科学基金(S2013010015957) |
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| 摘 要： | 在本文中，我们主要研究一类具有时滞的二元非线性积分不等式. 在不要求已知函数的单调性和可微性的条件下，通过将不等式中的函数单调化和积分号外函数作常量化的方法, 给出这类不等式中未知函数的估计, 并且以推论形式给出相应的一元积分不等式中未知函数的解的估计. 最后, 利用该估计证明了一类积分方程和一类微分方程的解的有界性.
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| 关 键 词： | 积分不等式 非线性函数 单调性 |
| 收稿时间： | 2014/12/3 0:00:00 |
| 修稿时间： | 2015/2/26 0:00:00 |
Generalizations of Integral Inequalities with Two Variables and their Applications |
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| ZHEN Bing,ZHONG Ji-Yu and DUAN Ying-Tao.Generalizations of Integral Inequalities with Two Variables and their Applications[J].Journal of Sichuan University (Natural Science Edition),2016,53(2):280-288. |
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| Authors: | ZHEN Bing ZHONG Ji-Yu and DUAN Ying-Tao |
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| Institution: | Department of Mathematics and Computation Science, Lingnan Normal University,Department of Mathematics and Computation Science, Lingnan Normal University; College of Mathematics, Sichuan University and Department of Mathematics and Computation Science, Lingnan Normal University |
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| Abstract: | In this paper, we discuss a retarded nonlinear integral inequality with two variables. By using the techniques of monotonization and reducing the function outside the integral to constant, we give an estimation of the unknown function in the inequality. Finally, by applying our result, we prove that the solutions of two types of equations, one are integral equations and the other differential equations, are bounded. |
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| Keywords: | integral inequality nonlinear function monotonicity |
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