一阶时滞差分方程周期边值问题的单调迭代法

Abstract

Abstract:

In this paper, the upper and lower solutions combining with the monotone iterative technique is emploied to study the existence of solutions for first order periodic boundary value problems of delay difference equations. Assuming that the upper and lower solutions exist, two group of sufficient conditions are obtained to guarantee the existence of extreme solutions of the boundary value problem.

Key words: Boundary value problem, Periodic solution; Upper and lower solutions, Existence, Monotone iterative technique

CLC Number:

34K10

SHU Yao-Liang, WENG Pei-Xuan. Monotone Method for First Order Periodic Boundary Value Problems of Delay Difference Equations[J].Acta mathematica scientia,Series A, 2005, 25(6): 869-876.

Trendmd

References

[1]Haddock J R,Nkashama M N.Periodic boundary value problems and monotone iterative methods for functional differential equations.Nonlinear Anal,1994,22: 267-276

[2]Jiang D,Wei J. Monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations.
Nonlinear Analysis,2002,50: 885-898

[3]Nieto J J, Jiang Y,Yan J R. Monotone iterative method for functional differential equations.Nonlinear Anal,1998,32: 741-747

[4]Nieto J J, Rodrguez Lopez R. Existence and approximation of s olutions for nonlinear functionaldifferentialequations with periodic boundary value conditions. Comput Math Appl, 2000,40: 433-442

[5]Ladde G S,Lakshmikantham V,Vatsala A S.Monotone Iterative Techniques for Nonlinear Differential Equations.London Pitman Advanced Publishing Program,1985

[6]Leela S, Oguztoreli M N.Periodic boundary value problems for differential equations with delay and monotone iterative methods.J Math Anal Appl,1987, 122: 301-307

[7]Liz E,Nieto J J. Periodic boundary value problems for a cla ss of functional differential equations. J Math Anal Appl, 1996,200: 680-686

[8]Agarwal R P.Difference Equations and Inequalities.New York: Marcel Dekker, 1992

[9]Cabada A,Otero Espinar V. Optimal existence results for nth order periodic boundary value difference equations.J Math Anal Appl,2000,247: 67-86

[10]Lakshmikantham V, Trigante D.Theory of Difference Equations: Nummerical Methods and Applications.Mathematics in Science and Engineering.Bostan Academic Press,1988

[11]Zhuang W, Chen Y, Cheng S S. Monotone methods for a discrete boundary value problems.Comput Math Appl,1996, 32: 41-49

[12]Pang Y H, Agarwal R P. Periodic boundary value problems for first and s econd order discrete systems. Mathl Comput Modelling,1992, 16: 101-112

[13]Pang Y H, Agarwal R P. Monotone iterative methods for a general class of discrete boundary value problems.Computers Math Applic, 1994, 28: 243-254

[14]Wang Y M. Monotone methods for a boundary value problem of second discrete equations. Computers Math Applic,1998, 36: 77-92

[15]Wang Y M. Monotone enclosure for a class of discrete boundary value problems without monotone nonlinearities.Computers Math Applic,1998, 35: 51-60

[16]Wang Y M, Agarwal R P. Remarks on periodic boundary value problems of first order discrete systems. Intern J Computer Math, 2000, 73: 493-502

Monotone Method for First Order Periodic Boundary Value Problems of Delay Difference Equations

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Wang Jun, Wang Tianlu, Wen Yanhua, Zhou Xianfeng. Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay [J]. Acta mathematica scientia,Series A, 2018, 38(5): 903-910.
[2]	Wang Huiwen, Zeng Hongjuan, Li Fang. An Existence Result for Impulsive Boundary Value Problem for Fractional Differential Equations with Multiple Base Points [J]. Acta mathematica scientia,Series A, 2018, 38(4): 697-715.
[3]	Lin Jiaoyan. Uniform Estimates in Time for the Solution to a Fluid-Particle Model [J]. Acta mathematica scientia,Series A, 2018, 38(3): 565-570.
[4]	Xing Chao, Ren Mengzhang, Luo Hong. The Existence of Global Weak Solutions to Thermohaline Circulation Equations [J]. Acta mathematica scientia,Series A, 2018, 38(2): 284-290.
[5]	Zhang Shuqin, Hu Lei. Initial Value Problem for Nonlinear Fractional Differential Equations with Variable-order Derivative and a Parameter [J]. Acta mathematica scientia,Series A, 2018, 38(2): 291-303.
[6]	Zhu Xincai. Existence of Constrained Minimizers for Schrödinger-Poisson Equations in R^N [J]. Acta mathematica scientia,Series A, 2018, 38(1): 61-70.
[7]	Ye Yaojun, Hu Yue. Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation [J]. Acta mathematica scientia,Series A, 2018, 38(1): 110-121.
[8]	Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.
[9]	Li Qin, Yang Zuodong. Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight [J]. Acta mathematica scientia,Series A, 2017, 37(5): 869-876.
[10]	Li Qingwei, Gao Wenjie, Han Yuzhu. Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity [J]. Acta mathematica scientia,Series A, 2017, 37(5): 877-894.
[11]	Huang Decheng, Chen Shouxin. New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations [J]. Acta mathematica scientia,Series A, 2017, 37(2): 299-306.
[12]	Chen Huiwen, Li Jianli, Shen Jianhua. New Results for Neumann Boundary Value Problem with Impulses via Variational Methods [J]. Acta mathematica scientia,Series A, 2017, 37(1): 54-61.
[13]	Qiu Hua, Zhang Yingshu, Fang Shaomei. The Global Existence Result of a Leray-α-Oldroyd Model to the Incompressible Viscoelastic Flow [J]. Acta mathematica scientia,Series A, 2017, 37(1): 102-112.
[14]	Yuan Hailong, Li Yanling. Existence and Stability of Coexistence States for a Lotka-Volterra Competition Model [J]. Acta mathematica scientia,Series A, 2017, 37(1): 173-184.
[15]	Zhang Hongwei, Liu Gongwei, Hu Qingying. Initial Boundary Value Problem for a Class Wave Equation with Logarithmic Source Term [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1124-1136.