利用拟线性化方法,讨论了Banach空间中一类二阶泛函微分方程初值问题解的收敛性,获得了解的平方收敛性结果.
The quasilinearization method is applied to discuss the convergence of the solutions for a class of second-order functional differential equations with initial condition in Banach space. We obtain the solutions for quadratic convergence of the approximate solutions.
[1] BHASKAR T G,LAKSHMIKANTHAM V,DEVI J V.Monotone iterative technique for functional differential equations with retardation and anticipation[J].Nonlinear Analysis,2007,66(10):2237-2242.
[2] WANG P G,WU H X,WU Y H.A note on monotone iterative technique for functional differential systems with retardation and anticipation[J].International Journal of Pure and Applied Mathematics,2007,41(5):749-754.
[3] 王培光,高玮.集值微分方程初值问题的拟线性化方法[J].河北大学学报(自然科学版),2011,31(1):1-6. WANG P G, GAO W.Quasilinearization of an initial value problem for set differential equations[J]. Journal of Hebei University(Natural Science Edition),2011,31(1):1-6.
[4] JANKOWSKI T.Functional differential equations of second order[J].Bull Belg Math Soc,2003,10:291-298.
[5] 陈改平.具有滞后与超前的泛函微分方程的拟线性化方法[D].保定:河北大学,2011. CHEN G P.Qvasilinearliation method for a class of funetional differential systems with retardation and anticijation[D].Baoding:Hebei university,2011.
[6] LE H H,LE T P N.Boundary and initial value problems for second-order neutral functional differential equations[J]. Electronic Journal of Differential Equations,2006,62:1-19.
[7] 郭大钧.非线性泛函分析[M].北京:高等教育出版社,2015.
[8] LAKSHMIKANTHAM V,VATSALA A S.Generalized quasilinearization for nonlinear problems[M].Dordrecht:Kluwer Academic Publishers,1998.
[9] 张恭庆,林源渠.泛函分析讲义[M].北京:北京大学出版社,2014.
