无限滞后测度泛函微分方程的解关于参数的可微性
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摘要
利用广义常微分方程解关于参数的可微性,建立无限滞后测度泛函微分方程解关于参数的可微性.
In this paper,we establish the differentiability of solutions with respect to parameters for measure functional differential equations with infinite delay by using the differentiability of solutions with respect to parameters for generalized ordinary differential equations.
In this paper,we establish the differentiability of solutions with respect to parameters for measure functional differential equations with infinite delay by using the differentiability of solutions with respect to parameters for generalized ordinary differential equations.
引文
[1]SLAVIK A.Measure functional differential equations with infinite delay[J].Nonlinear Analysis,2013,79(3):140-155.
[2]FEDERSON M,MESQUITA J G,SLAVK A.Measure functional differential equations and functional dynamic equations on time scales[J].J Differential Equations,2012,252(6):3816-3847.
[3]李宝麟,王保弟.无限滞后测度泛函微分方程的解关于初值条件的可微性[J].四川师范大学学报(自然科学版),2017,40(1):61-67.
[4]SLAVOK A.Generalized differential equations:differentiability of solutions with respect to initial conditions and parameters[J].JMath Anal Appl,2013,402(1):261-274.
[5]SCHWABIK S.Generalized Ordinary Differential Equations[M].Singapore:World Scientific,1992.
[6]李宝麟,刘丽丽,张元德,等.脉冲滞后泛函微分方程的解相对参数的可微性[J].河北师范大学学报(自然科学版),2015,39(6):461-467.
[7]HILSCHER R,ZEIDAN V,KRATZ W.Differentiation of solutions of dynamic equations on time scales with respect to parameters[J].Adv Dyn Syst Appl,2009,4(1):35-54.
[8]李宝麟,赵红岩,魏婷婷,等.Carathéodory系统的解相对于初值条件的可微性[J].西北师范大学学报(自然科学版),2016,52(3):14-17.
[9]张元德.测度微分方程解对参数的连续依赖性与解关于参数的可微性[D].兰州:西北师范大学,2016.
[10]李宝麟,王云凤.无限滞后测度泛函微分方程解的有界性[J].四川师范大学学报(自然科学版),2018,41(2):190-196.
[11]KELLEY W G.The Theory of Differential Equations[M].New York:Springer-Verlag,2010.
[12]KURZWEIL J.Generalized ordinary differential equations and continuous dependence on a parameter[J].Czechoslovak Math J,1957,7(82):418-449.
[13]KURZWEIL J.Generalized ordinary differential equations[J].Czechoslovak Math J,1958,83(8):360-388.
[14]FEDERSON M.MESQUITA J G.Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses[J].J Differential Equations,2013,255(10):3098-3126.
[15]徐远通.泛函微分方程与测度微分方程[M].广州:中山大学出版社,1988.
[16]SLAVIK A.Well-posedness results for abstract generalized differential equations and measure functional differential equations[J].J Differential Equations,2015,259(2):666-707.
[2]FEDERSON M,MESQUITA J G,SLAVK A.Measure functional differential equations and functional dynamic equations on time scales[J].J Differential Equations,2012,252(6):3816-3847.
[3]李宝麟,王保弟.无限滞后测度泛函微分方程的解关于初值条件的可微性[J].四川师范大学学报(自然科学版),2017,40(1):61-67.
[4]SLAVOK A.Generalized differential equations:differentiability of solutions with respect to initial conditions and parameters[J].JMath Anal Appl,2013,402(1):261-274.
[5]SCHWABIK S.Generalized Ordinary Differential Equations[M].Singapore:World Scientific,1992.
[6]李宝麟,刘丽丽,张元德,等.脉冲滞后泛函微分方程的解相对参数的可微性[J].河北师范大学学报(自然科学版),2015,39(6):461-467.
[7]HILSCHER R,ZEIDAN V,KRATZ W.Differentiation of solutions of dynamic equations on time scales with respect to parameters[J].Adv Dyn Syst Appl,2009,4(1):35-54.
[8]李宝麟,赵红岩,魏婷婷,等.Carathéodory系统的解相对于初值条件的可微性[J].西北师范大学学报(自然科学版),2016,52(3):14-17.
[9]张元德.测度微分方程解对参数的连续依赖性与解关于参数的可微性[D].兰州:西北师范大学,2016.
[10]李宝麟,王云凤.无限滞后测度泛函微分方程解的有界性[J].四川师范大学学报(自然科学版),2018,41(2):190-196.
[11]KELLEY W G.The Theory of Differential Equations[M].New York:Springer-Verlag,2010.
[12]KURZWEIL J.Generalized ordinary differential equations and continuous dependence on a parameter[J].Czechoslovak Math J,1957,7(82):418-449.
[13]KURZWEIL J.Generalized ordinary differential equations[J].Czechoslovak Math J,1958,83(8):360-388.
[14]FEDERSON M.MESQUITA J G.Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses[J].J Differential Equations,2013,255(10):3098-3126.
[15]徐远通.泛函微分方程与测度微分方程[M].广州:中山大学出版社,1988.
[16]SLAVIK A.Well-posedness results for abstract generalized differential equations and measure functional differential equations[J].J Differential Equations,2015,259(2):666-707.