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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 Ying1; Wang Faxing1; Gao 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 problem; topological degree; lower 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:

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Last Update: 2019-03-30