Existence and Uniqueness of Solutions for Initial Value Problems of Second Order Ordinary Differential Equations in Banach Space

Hong Shihuang; Hu Shigeng

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(3): 277-285

Hong Shihuang, Hu Shigeng. Existence and Uniqueness of Solutions for Initial Value Problems of Second Order Ordinary Differential Equations in Banach Space[J]. Applied Mathematics and Mechanics, 1999, 20(3): 277-285.

Citation:

PDF( 388 KB)

Existence and Uniqueness of Solutions for Initial Value Problems of Second Order Ordinary Differential Equations in Banach Space

Hong Shihuang¹,
Hu Shigeng²

1.
Hainan University, Haikou 570228, P. R. China;
2.
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Received Date: 1997-10-11
Rev Recd Date: 1998-10-05
Publish Date: 1999-03-15

Abstract

Abstract

In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.
- ordered Banach spaces,
- measures of noncompactness,
- mixed monotone operators

FullText(HTML)

References(10)

References

[1]	Ladde G S,Lakshmikantham V,Vatsala A S.Monotone Iterative Technique for Nonlinear Differential Equations[M].Boston:Pitman Publishing,1985
[2]	Khavania M,Lakshmikantham V.The method of mixed monotony and first order differential systems[J].Nonlinear Anal.1986,10(9):873～877
[3]	Lakshmikantham V.Periodic boundary value problems of first and second order differential equations[J].J Appl Math Simulation,1989,2(3):131～138
[4]	Heikkil S,Kumpulainen M,Lakshmikantham V.On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems lnvolving discontinuous[J].J Appl Math Stochastic Analysis,1992,5(1):1～17
[5]	Heikkil S,Leela S.On the solvability of the second order initial value problems in Banach spaces[J].Dynamic Systems and Appl,1992,1(2):141～170
[6]	Heikkil S,Lakshmikantham V.On the second order mixed quasimonotone periodic boundary value systems in ordered Banach spaces[J].Nonl Anal,1993,20(9):1135～1144
[7]	Lakshmikantham V,Leela S,Farzana A Mcrae.Improved generalized quasiliearization method[J].Nonl Anal,1995,24(5):1627～1637
[8]	Hristova S G,Bainov D D.Monotone-iterative techniques of V Lakshmikantham for a boundary value problem for systems of impulsive differential-difference equations[J].J Math Anal Appl,1996,197(1):1～13
[9]	胡适耕,非线性分析[M].武汉:华中理工大学出版社,1996
[10]	Deimling K.Nonlinear Functional Analysis[M],Berling:Springer-Verlag,1985