Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem
Joint Authors
Tariboon, Jessada
Sitthiwirattham, Thanin
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-09
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem Δ2u(t-1)+a(t)f(u(t))=0, t∈{1,2,…,T}, u(0)=β∑s=1ηu(s), u(T+1)=α∑s=1ηu(s), where f is continuous, T≥3 is a fixed positive integer, η∈{1,2,...,T-1}, 0<α<(2T+2)/η(η+1), 0<β<(2T+2-αη(η+1))/η(2T-η+1), and Δu(t-1)=u(t)-u(t-1).
We show the existence of at least one positive solution if f is either superlinear or sublinear.
American Psychological Association (APA)
Sitthiwirattham, Thanin& Tariboon, Jessada. 2012. Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-993379
Modern Language Association (MLA)
Sitthiwirattham, Thanin& Tariboon, Jessada. Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem. Journal of Applied Mathematics No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-993379
American Medical Association (AMA)
Sitthiwirattham, Thanin& Tariboon, Jessada. Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-993379
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993379