广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (2): 48-53.

• • 上一篇    下一篇

具p-Laplacian算子时滞微分方程边值问题解的存在唯一性

韦煜明, 王勇, 唐艳秋, 范江华   

  1. 广西师范大学数学科学学院,广西桂林541004
  • 收稿日期:2011-12-20 出版日期:2012-06-20 发布日期:2018-12-03
  • 通讯作者: 韦煜明(1974—),男,广西桂平人,广西师范大学副教授,博士。E-mail:ymwei@mailbox.gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11061006,61074049);广西教育厅科研项目(201012MS025)

Existence and Uniqueness of Solutions for Delay Boundary Value Problems with p-Laplacian on Infinite Intervals

WEI Yu-ming, WANG Yong, TANG Yan-qiu, FAN Jiang-hua   

  1. College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2011-12-20 Online:2012-06-20 Published:2018-12-03

摘要： 本文主要研究无穷区间上具有p-Laplacian算子的时滞微分方程边值问题解的存在性和唯一性,利用Schauder不动点定理得到解的存在性,由Banach压缩映射原理证明解的唯一性,并给出一个例子来说明主要结果的应用。

关键词: 时滞微分方程, 边值问题, 不动点定理, 无限区间

Abstract: This paper is concerned with the existence and uniqueness of solutions for boundary value problems with p-Laplacian delay differential equations on the half-line.The existence of solutions is derived from the Schauder's fixed point theorem,whereas the uniqueness of solution is established by the Banach's contraction principle.An example is given to demonstrate the main results of its application.

Key words: delay differential equation, boundary value problem, fixed point theorem, infinite interval

中图分类号: 

  • O175.1
[1] AGARWAL R P,O'REGAN D.An infinite interval problem arising in circularly symmetric deformations of shallow membrane caps[J].International Journal of Nonlinear Mechanics,2004,39(5):779-784.
[2] DRIVER R D.Ordinary and delay differential equations[M].New York:Springer-Verlag,1977.
[3] AGARWAL R P.O'REGAN D.Infinite interval problems for differential,difference and integral equations[M].Dordrecht:Kluwer Academic Publishers,2001.
[4] AGARWAL R P,O'REGAN D,WONG P J Y.Positive solutions of differential,difference and integral equations[M].Dordrecht:Kluwer Academic Publishers,1999.
[5] BAI Ding-yong,XU Yuan-tong.Existence of positive solutions forboundary value problems of second order delay differential equations[J].Applied Mathematics Letters,2005,18(6):621-630.
[6] AGARWAL R P,PHILOS C G,TSAMATOS P C.Global solutions of a singular initial value problem to second order nonlinear delay differential equations[J].Mathematical and Computer Modelling,2006,43(7/8):854-869.
[7] BAI Chuan-zhi,FANG Jin-xuan.On positive solutions of boundary value problems forsecond-order functional differential equations on infinite intervals[J].JMath Anal Appl,2003,282(2):711-731.
[8] HALE J K,LUNEL S M V.Introduction to functional differential equations[M].New York:Springer-Verlag,1993.
[9] MAVRIDIS K G,PHILOS C G,TSAMATOS P C.Multiple positive solutionsfor a second order delay boundary value problem on the half-line[J].AnnalesPolonici Mathematici,2006,88(2):173-191.
[10] 韦煜明,杜波,葛渭高.无穷区间上二阶时滞微分方程边值问题解的存在性[J].徐州师范大学学报:自然科学版,2008,26(2):26-29.
[11] 张恭庆,林源渠.泛函分析讲义[M].北京:北京大学出版社,1987.
[12] AVRAMESCU C.Sur l'existence des solutions convergentes des systemes d'équations différentielles non linéaires[J].Ann Mat Pura Appl,1969,81(1):147-168.
[13] MAVRIDIS K G,PHILOS C G,TSAMATOS P C.Existence of solutions ofa boundary value problem on the half-line to second order nonlinear delay differential equations[J].Arch Math,2006,86(2):163-175.
[14] BANACH S.Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales[J].Fund Math,1922,3:133-181.
[1] 黄燕萍, 韦煜明. 一类分数阶微分方程多点边值问题的多解性[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 41-49.
[2] 闫荣君, 韦煜明, 冯春华. 带p-Laplacian算子的时滞分数阶微分方程边值问题3个正解的存在性[J]. 广西师范大学学报（自然科学版）, 2017, 35(3): 75-82.
[3] 章美月. 关于电子束聚焦系统模型的一些新结果[J]. 广西师范大学学报（自然科学版）, 2015, 33(1): 38-44.
[4] 薛晋栋, 冯春华. 一类时滞脉冲微积分方程的正概周期解[J]. 广西师范大学学报（自然科学版）, 2012, 30(4): 48-53.
[5] 郝平平, 冯春华. 一类具有非线性物种密度制约死亡率的Nicholson模型解的性态[J]. 广西师范大学学报（自然科学版）, 2012, 30(2): 42-47.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发