Banach空间中二阶时滞微分方程的单调迭代技巧
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摘要
借助Banach空间中二阶线性微分方程的周期解的存在性与唯一性定理,运用上下解的单调迭代技巧,讨论了有序Banach空间中二阶多时滞微分方程的ω-周期解的存在性与唯一性.所得的结果推广了常微分方程的有关结论.
With the existence and uniqueness of periodic solutions for the second-order linear differential equation in Banach spaces E,the existence and uniqueness ofω-periodic solutions for the second-order differential equation with multiple delays in Banach spaces Eare discussed by using the monotone iterative technique in presence of upper and lower solutions.The relevant results of ordinary differential equations are extended.
With the existence and uniqueness of periodic solutions for the second-order linear differential equation in Banach spaces E,the existence and uniqueness ofω-periodic solutions for the second-order differential equation with multiple delays in Banach spaces Eare discussed by using the monotone iterative technique in presence of upper and lower solutions.The relevant results of ordinary differential equations are extended.
引文
[1]LI Y.Positive periodic solutions of second-order differential equations with delays[J].Abstract&Applied Analysis,2012:509-512.
[2]李玉玉.Banach空间中二阶时滞微分方程的周期解[J].兰州文理学院学报(自然科学版),2016,30(4):27-31.
[3]李玉玉.有序Banach空间二阶时滞微分方程的正周期解[J].西北师范大学学报(自然科学版),2017,53(1):5-11.
[4]刘旭,周文学.二阶脉冲泛函微分方程周期边值问题的单调迭代技巧[J].兰州交通大学学报,2007,26(1):138-141.
[5]JIANG D,WEI J.Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations[J].Nonlinear Analysis,2002,50:885-898.
[6]JIANG D,NIETO J J,ZUO W.Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations[J].Journal of Mathematical Analysis&Applications,2004,289(2):691-699.
[7]WENG P,JIANG D.Existence of positive solutions for boundary value problem of second-order FDE[J].Comput.Math.Appl.,1999,37:1-9.
[8]LI Y.Periodic solutions of a periodic deyal predatorprey system[J].Proceedings of the American Mathematical Society,1999,127(5):1331-1335.
[9]李永祥.Banach空间二阶微分方程的周期解[J].西北师范大学学报(自然科学版),1998,34(2):10-13.
[10]李永祥.二阶非线性常微分方程的正周期解[J].数学学报,2002,45(3):481-488.
[11]郭大钧,孙经先.抽象空间常微分方程[M].济南:山东科学技术出版社,2005.
[12]HEINZ H P.On the behaviour of measure of noncompactness with respect to differention and integration of vector-valued functions[J].Nonlinear Analysis Theory Methods&Applications,1983,7(12):1351-1371.
[2]李玉玉.Banach空间中二阶时滞微分方程的周期解[J].兰州文理学院学报(自然科学版),2016,30(4):27-31.
[3]李玉玉.有序Banach空间二阶时滞微分方程的正周期解[J].西北师范大学学报(自然科学版),2017,53(1):5-11.
[4]刘旭,周文学.二阶脉冲泛函微分方程周期边值问题的单调迭代技巧[J].兰州交通大学学报,2007,26(1):138-141.
[5]JIANG D,WEI J.Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations[J].Nonlinear Analysis,2002,50:885-898.
[6]JIANG D,NIETO J J,ZUO W.Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations[J].Journal of Mathematical Analysis&Applications,2004,289(2):691-699.
[7]WENG P,JIANG D.Existence of positive solutions for boundary value problem of second-order FDE[J].Comput.Math.Appl.,1999,37:1-9.
[8]LI Y.Periodic solutions of a periodic deyal predatorprey system[J].Proceedings of the American Mathematical Society,1999,127(5):1331-1335.
[9]李永祥.Banach空间二阶微分方程的周期解[J].西北师范大学学报(自然科学版),1998,34(2):10-13.
[10]李永祥.二阶非线性常微分方程的正周期解[J].数学学报,2002,45(3):481-488.
[11]郭大钧,孙经先.抽象空间常微分方程[M].济南:山东科学技术出版社,2005.
[12]HEINZ H P.On the behaviour of measure of noncompactness with respect to differention and integration of vector-valued functions[J].Nonlinear Analysis Theory Methods&Applications,1983,7(12):1351-1371.