含有Henstock-Kurzweil-Stieltjes积分的积分方程的解的存在性
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摘要
本文中用非紧性测度方法和Darbo不动点定理,研究一类含Henstock-Kurzweil-Stieltjes积分的积分方程的解的存在性.同时,提供一个例子说明我们的结果.
In this work,we applied the method associated with the technique of measure of noncompactness and the Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile,an example is provided to illustrate our results.
In this work,we applied the method associated with the technique of measure of noncompactness and the Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile,an example is provided to illustrate our results.
引文
[1]Alvarez E,Lizama C.Application of measure of noncompactness to Volterra equations of convolution type[J].J Integral Equations Appl,2016,28(4):441-458.
[2]Banas J,Paslawska-P M.Monotonic solutions of Urysohn integral equation on unbounded interval[J].Comput Math Appl,2004,47(12):1947-1954.
[3]Schwabik S,Ye G J.Topics in Banach space integration[M].Singapore:World Scientific,2005.
[4]Kurzweil J.Generalized ordinary differential equations and continuous dependence on a parameter[J].Czechoslovak Math J,1957,7(82):418-449.
[5]Lee P Y.Lanzhou lectures on Henstock integration[M].Singapore:World Scientific,1989.
[6]Krejci P.The Kurzweil integral and hysteresis[J].J Phys:Conf Ser,2006,55:144-154.
[7]Heikkila S,Ye G J.Equations containing locally Henstock-Kurzweil integrable functions[J].Appl Math 2012,57(6):569-580.
[8]Chew T S.On Kurzweil generalized ordinary differentialequations[J].J Differential Equations,1988,76(2):286-293.
[9]Chew T S,Flordeliza F.On x'=f(t,x)and Henstock-Kurzweil integrals[J].Differential Integral Equations,1991,4(4):861-868.
[10]Ye G J,Liu W.The distributional Henstock-Kurzweil integral and applications[J].Monatsh Math,2016,181(4):975-989.
[11]Kaczor W.Measures of noncompactness and an existence theorem for differential equations in Banach space[J].Ann Univ Mariae Curie-sklodowska sect,1988,42(A):35-40.
[12]Mursaleen M.Differential equations in classical sequence spaces[J].Rev R Acad Cienc Exactas Fis Nat Ser A Math RACSAM,2017,111(2):587-612.
[13]Kazemi M,Ezzati R.Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness[J].Appl Math Comput,2016,275:165-171.
[14]Dovgoshey O,Martio O,Ryazanov V,et al.The Cantor function[J].Expo Math,2006,24(1):1-37.
[2]Banas J,Paslawska-P M.Monotonic solutions of Urysohn integral equation on unbounded interval[J].Comput Math Appl,2004,47(12):1947-1954.
[3]Schwabik S,Ye G J.Topics in Banach space integration[M].Singapore:World Scientific,2005.
[4]Kurzweil J.Generalized ordinary differential equations and continuous dependence on a parameter[J].Czechoslovak Math J,1957,7(82):418-449.
[5]Lee P Y.Lanzhou lectures on Henstock integration[M].Singapore:World Scientific,1989.
[6]Krejci P.The Kurzweil integral and hysteresis[J].J Phys:Conf Ser,2006,55:144-154.
[7]Heikkila S,Ye G J.Equations containing locally Henstock-Kurzweil integrable functions[J].Appl Math 2012,57(6):569-580.
[8]Chew T S.On Kurzweil generalized ordinary differentialequations[J].J Differential Equations,1988,76(2):286-293.
[9]Chew T S,Flordeliza F.On x'=f(t,x)and Henstock-Kurzweil integrals[J].Differential Integral Equations,1991,4(4):861-868.
[10]Ye G J,Liu W.The distributional Henstock-Kurzweil integral and applications[J].Monatsh Math,2016,181(4):975-989.
[11]Kaczor W.Measures of noncompactness and an existence theorem for differential equations in Banach space[J].Ann Univ Mariae Curie-sklodowska sect,1988,42(A):35-40.
[12]Mursaleen M.Differential equations in classical sequence spaces[J].Rev R Acad Cienc Exactas Fis Nat Ser A Math RACSAM,2017,111(2):587-612.
[13]Kazemi M,Ezzati R.Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness[J].Appl Math Comput,2016,275:165-171.
[14]Dovgoshey O,Martio O,Ryazanov V,et al.The Cantor function[J].Expo Math,2006,24(1):1-37.