|Table of Contents|

Upper and Lower Solutions and Topological Degree inDifference Equations Boundary Value Problems(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2019年01期
Page:
36-
Research Field:
·数学·
Publishing date:

Info

Title:
Upper and Lower Solutions and Topological Degree inDifference Equations Boundary Value Problems
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)
Keywords:
discrete boundary value problemtopological degreelower and upper solutions
PACS:
O175.14
DOI:
10.3969/j.issn.1001-4616.2019.01.007
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.

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.

Memo

Memo:
-
Last Update: 2019-03-30