| Kurzweil方程的强收敛性（英） |
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| 引用本文： | 马学敏,张玲,李宝麟. Kurzweil方程的强收敛性（英）[J]. 工程数学学报, 2020, 37(1): 107-120. DOI: 10.3969/j.issn.1005-3085.2020.01.009 |
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| 作者姓名： | 马学敏 张玲 李宝麟 |
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| 作者单位： | 1- 甘肃中医药大学理科教学部，甘肃定西7430002- 西北师范大学数学与信息科学学院，兰州730070 |
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| 基金项目： | The National Natural Science Foundation of China(10771171);the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC);the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)~~ |
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| 摘 要： | 本文利用 Kurzweil 积分理论和 $Phi$-有界变差函数理论，讨论了 Kurzweil 方程的强收敛性及其在常微分方程序列中的应用．得到 Kurzweil 方程 $Phi$-有界变差解的强收敛性定理，该结果是对 Kurzweil 方程 $Phi$-有界变差解对参数的连续依赖性性质的延续，并且是对已有的 Kurzweil 方程的有界变差解的强收敛性定理的本质推广．
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| 关 键 词： | Kurzweil 方程 强收敛性 $Phi$-有界变差函数 |
| 收稿时间： | 2017-11-06 |
Emphatic Convergence for Kurzweil Equations |
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| MA Xue-min,ZHANG Ling,LI Bao-lin. Emphatic Convergence for Kurzweil Equations[J]. Chinese Journal of Engineering Mathematics, 2020, 37(1): 107-120. DOI: 10.3969/j.issn.1005-3085.2020.01.009 |
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| Authors: | MA Xue-min ZHANG Ling LI Bao-lin |
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| Affiliation: | 1- Teaching Department of Science, Gansu University of Chinese Medicine, Dingxi, Gansu 743000;2- College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070 |
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| Abstract: | In this paper,by using the theories of Kurzweil integral and boundedΦ-variation function.Emphatic convergence for Kurzweil equations and its application for a sequence of ordinary differential equations are discussed.The theorem of emphatic convergence for boundedΦ-variation solutions of Kurzweil equations is obtained.The result is continuation of continuous dependence of boundedΦ-variation solutions on parameters for Kurzweil equations and essential generalization of the emphatic convergence for bounded variation solutions of Kurzweil equations. |
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| Keywords: | Kurzweil equations emphatic convergence boundedΦ-variation function |
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