在线阅读 --自然科学版 2019年2期《关于分布微分方程的柯西问题》
关于分布微分方程的柯西问题--[在线阅读]
程蓉, 叶国菊, 刘尉, 赵大方
河海大学 理学院, 江苏 南京 211100
起止页码: 93--98页
DOI: 10.13763/j.cnki.jhebnu.nse.2019.02.001
摘要
利用Schauder不动点定理和Gronwall-Bellman不等式研究了含Kurzweil-Henstock-Stieltjes积分的一阶分布微分方程解的存在性及唯一性.最后给出了一个例子说明结论的普遍性.

On Cauchy Problem for Distributional Differential Equation
CHENG Rong, YE Guoju, LIU Wei, ZHAO Dafang
College of Science, Hohai University, Jiangsu Nanjing 211100, China
Abstract:
In this paper, we study the existence and uniqueness of solutions of first-order distributional differential equation involving the Kurzweil-Henstock-Stieltjes integral.The proof of the existence and uniqueness results is based on Schauder's fixed point theorem and Gronwall-Bellman inequality.Meanwhile, an example is given to illustrate the universality of the results.

收稿日期: 2018-09-07
基金项目: 中央高校基本科研业务费专项资金(2017B19714,2017B07414)

参考文献:
[1]CICHOH M,SATCP B.Measure Differential Inclusions-between Continuous and Discrete[J].Adv Difference Equ,2014(1):56.doi:10.1186/1687-1847-2014-56
[2]SATCO B.Regulated Solutions for Nonlinear Measure Driven Equations[J].Nonlinear Anal Hybrid Syst,2014(913):22-31.doi:10.1016/j.nahs.2014.02.001
[3]CAO Y,SUN J.On the Existence of Nonlinear Measure Driven Equations Involving Non-absolutely Convergent Integrals[J].Nonlinear Anal Hybrid Syst,2016(20):72-81.doi:10.1016/j.nahs.2015.11.003
[4]HǒNIG C S.Volterra-stieltjes Integral Equations with Linear Constraints and Discontinuous Solutions[J].Bull Amer Math Soc,1975(81):593-598.doi:10.1090/S0002-9904-1975-13749-9
[5]FRAŇKOVÁ D.Regulated Functions[J].Math Bohem,1991,116(1):20-59.
[6]KURZWEIL J.Generalized Ordinary Differential Equations and Continuous Dependence on a Parameter Czechoslovak[J].Math J,1957,7(82):418-449.
[7]KREJAKČÍ P.The Kurzweil Integral with Exclusion of Negligible Sets[J].Math Bohem,2003,128(3):277-292.
[8]SCHWABIK Š.Generalized Ordinary Differential Equations[M].Singapore:World Scientific,1992.doi:10.1142/1875
[9]KREJAKČÍ P,LIERO M.Rate Independent Kurzweil Processes[J].Appl Math,2009,54(2):117-145.doi:10.1007/s10492-009-0009-5
[10]LEE P Y.Lanzhou Lectures on Henstock Integration[M].Singapore:World Scientific,1989.doi:10.1142/0845
[11]DING X,YE G.Generalized Gronwall-Bellman Inequalities Using the Henstock-kurzweil Integral[J].Southeast Asian Bull Math,2009,33(4):703-713.
[12]LIU W,YE G,WANG Y,et al.On Periodic Solutions for First-order Differential Equations Involving the Distributional Henstock-kurzweil Integral[J].Bull Aust Math Soc,2012,86(2):327-338.doi:10.1017/S00049727/1003455
[13]HARDY G H.Weierstrass's Non-diefferentiable Function[J].Trans Amer Math Soc,1916,17(3):301-325.doi:10.1090/S0002-9947-1916-1501044-1
[14]SCHMAEDEKE W W.Optimal Control Theory for Nonlinear Vector Differential Equations Containing Measures[J].SIAM Control,1965,3:231-280.doi:10.1137/0303019
[15]DAS P C,SHARMA R R.On Optimal Controls for Measure Delay-differential Equations[J].SIAM Control,1971(9):43-61.doi:10.1137/0309005