[1]郑 莹,王发兴,高广花.微分方程边值问题中的上、下解及拓扑度[J].南京师范大学学报(自然科学版),2019,42(01):36.[doi:10.3969/j.issn.1001-4616.2019.01.007]
 Zheng Ying,Wang Faxing,Gao Guanghua.Upper and Lower Solutions and Topological Degree inDifference Equations Boundary Value Problems[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(01):36.[doi:10.3969/j.issn.1001-4616.2019.01.007]
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微分方程边值问题中的上、下解及拓扑度()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第42卷
期数:
2019年01期
页码:
36
栏目:
·数学·
出版日期:
2019-03-20

文章信息/Info

Title:
Upper and Lower Solutions and Topological Degree inDifference Equations Boundary Value Problems
文章编号:
1001-4616(2019)01-0036-09
作者:
郑 莹1王发兴1高广花2
(1.南京邮电大学通达学院,江苏 扬州 225127)(2.南京邮电大学理学院,江苏 南京 210046)
Author(s):
Zheng Ying1Wang Faxing1Gao Guanghua2
(1.Tongda College of Nanjing University of Posts and Telecommunications,Yangzhou 225127,China)(2.College of Science,Nanjing University of Posts & Telecommunications,Nanjing 210046,China)
关键词:
离散边值问题拓扑度上、下解
Keywords:
discrete boundary value problemtopological degreelower and upper solutions
分类号:
O175.14
DOI:
10.3969/j.issn.1001-4616.2019.01.007
文献标志码:
A
摘要:
研究了不同边界条件的二阶非线性微分方程Δ2u(t-1)=f(t,u(t)),t∈[1,T]. 其中f:[1,T]×R→R是连续的,T≥1是一个固定的自然数. 首先,我们研究了顺序上、下解的情况. 然后研究了逆序上、下解的情况. 并且证明了在这两种情况下,拓扑度与严格上、下解之间的关系,利用这个关系我们得到了离散边值问题的存在性.
Abstract:
This paper deals with second order nonlinear difference equation Δ2u(t-1)=f(t,u(t)),t∈[1,T]with different boundary conditions,where f:[1,T]×R→R is continuous,T≥1 a fixed natural number. Firstly,we consider the case of well order lower and upper solutions. Secondly,we investigate the case of upper and lower solutions having the opposite ordering. We prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence results for the discrete boundary value problems under consideration.

参考文献/References:

[1] IRENA R. Upper and lower solutions and topological degree[J]. J Math Anal Appl,1999,234:311-327.
[2]YULIAN A. Existence of solutions for a three-point boundary value problem at resonance[J]. Nonlinear analysis,2006,65:1633-1643.
[3]FANGFEI L,MEI J,XIPING L,et al. Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order[J]. Nonlinear analysis,2007,68:2381-2383.
[4]CABADA A A,MINH’ OS F M. Fully nonlinear fourth-order equations with funtions[J]. J Math Anal Appl,2007,340:239-251.
[5]IRENA RR,CHRISTOPHER C T. Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions[J]. Nonlinear analysis,2007,67:1236-1245.
[6]TIAN Y,TISDELL,CHRISTOPHER C W. The method of upper and lower solutions for discrete BVP on infinite intervals[J]. Journal of difference equations and applications,2011,17-3:267-278.
[7]ZHAO Y L,CHEN H B,XU C J. Existence of multiple solutions for three-point boundary-value problems on infinite intervals in Banach spaces[J]. Electronic journal of differential equations,2012,44:1-11.
[8]HE Z M,ZHANG X M. Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions[J]. Applied mathematics and computation,2004,156:605-620.
[9]CABADA A,OTERO-ESPINAR V. Fixed sign solutions of second-order difference equations with neumann boundary conditions[J]. Computers and mathematics with applications,2003,45:1125-1136.
[10]LI Y X. Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations[J]. J Math Anal Appl,2007,327:997-1009.
[11]WANG H Z,RICHARD M,TIMONEY. Upper and lower solutions method for second order boundary value problems with delay[J]. Acta mathematica sinica,2010,3:489-494.
[12]YANG J,SONG N N,JIN Y.Upper and lower solution method for fourth order four point boundary value problem on time scales[J]. Mathematics in practice and theory,2013,21:205-211.

备注/Memo

备注/Memo:
收稿日期:2017-09-01.
基金项目:国家自然科学青年基金项目(11401319).
通讯联系人:王发兴,副教授,研究方向:泛函分析,微分方程. E-mail:wangfx@njupt.edu.cn
更新日期/Last Update: 2019-03-30