Bounded Positive Solutions for a Third Order Discrete Equation

This paper studies the following third order neutral delay discrete equation Δ(anΔ2(xn+pnxn-τ))+f(n,xn-d1n,…,xn-dln)=gn,n≥n0, where τ,l∈ℕ, n0 ∈ℕ∪{0}, {an}n∈ℕn0, {pn}n∈ℕn0, {gn}n∈ℕn0 are real sequences with an≠0 for n≥n0, {din}n∈ℕn0⊆ℤ with lim n→∞(n-din)=+∞ for i∈{1,2,…,l} and f∈C(ℕn0×ℝl,ℝ). By using...

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Main Authors:	Zeqing Liu, Ming Jia, Shin Min Kang, Young Chel Kwun
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2012/237036

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spelling	doaj-292581cadc074861975e4d03e91480de2020-11-24T20:50:54ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/237036237036Bounded Positive Solutions for a Third Order Discrete EquationZeqing Liu0Ming Jia1Shin Min Kang2Young Chel Kwun3Liaoning Normal University, Department of Mathematics, Dalian, Liaoning 116029, ChinaDalian Hongwen Middle School, Dalian, Liaoning 116029, ChinaGyeongsang National University, Department of Mathematics and RINS, Jinju 660-701, Republic of KoreaDong-A University, Department of Mathematics, Pusan 614-714, Republic of KoreaThis paper studies the following third order neutral delay discrete equation Δ(anΔ2(xn+pnxn-τ))+f(n,xn-d1n,…,xn-dln)=gn,n≥n0, where τ,l∈ℕ, n0 ∈ℕ∪{0}, {an}n∈ℕn0, {pn}n∈ℕn0, {gn}n∈ℕn0 are real sequences with an≠0 for n≥n0, {din}n∈ℕn0⊆ℤ with lim n→∞(n-din)=+∞ for i∈{1,2,…,l} and f∈C(ℕn0×ℝl,ℝ). By using a nonlinear alternative theorem of Leray-Schauder type, we get sufficient conditions which ensure the existence of bounded positive solutions for the equation. Three examples are given to illustrate the results obtained in this paper.http://dx.doi.org/10.1155/2012/237036
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun
spellingShingle	Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun Bounded Positive Solutions for a Third Order Discrete Equation Abstract and Applied Analysis
author_facet	Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun
author_sort	Zeqing Liu
title	Bounded Positive Solutions for a Third Order Discrete Equation
title_short	Bounded Positive Solutions for a Third Order Discrete Equation
title_full	Bounded Positive Solutions for a Third Order Discrete Equation
title_fullStr	Bounded Positive Solutions for a Third Order Discrete Equation
title_full_unstemmed	Bounded Positive Solutions for a Third Order Discrete Equation
title_sort	bounded positive solutions for a third order discrete equation
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2012-01-01
description	This paper studies the following third order neutral delay discrete equation Δ(anΔ2(xn+pnxn-τ))+f(n,xn-d1n,…,xn-dln)=gn,n≥n0, where τ,l∈ℕ, n0 ∈ℕ∪{0}, {an}n∈ℕn0, {pn}n∈ℕn0, {gn}n∈ℕn0 are real sequences with an≠0 for n≥n0, {din}n∈ℕn0⊆ℤ with lim n→∞(n-din)=+∞ for i∈{1,2,…,l} and f∈C(ℕn0×ℝl,ℝ). By using a nonlinear alternative theorem of Leray-Schauder type, we get sufficient conditions which ensure the existence of bounded positive solutions for the equation. Three examples are given to illustrate the results obtained in this paper.
url	http://dx.doi.org/10.1155/2012/237036
work_keys_str_mv	AT zeqingliu boundedpositivesolutionsforathirdorderdiscreteequation AT mingjia boundedpositivesolutionsforathirdorderdiscreteequation AT shinminkang boundedpositivesolutionsforathirdorderdiscreteequation AT youngchelkwun boundedpositivesolutionsforathirdorderdiscreteequation
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Bounded Positive Solutions for a Third Order Discrete Equation

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