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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/237036 |
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| author | Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun |
| author_facet | Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-292581cadc074861975e4d03e91480de |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-292581cadc074861975e4d03e91480de2025-02-03T01:31:56ZengWileyAbstract 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 |
| spellingShingle | Zeqing Liu Ming Jia Shin Min Kang Young Chel Kwun Bounded Positive Solutions for a Third Order Discrete Equation Abstract and Applied Analysis |
| title | 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_short | Bounded Positive Solutions for a Third Order Discrete Equation |
| title_sort | bounded positive solutions for a third order discrete equation |
| url | http://dx.doi.org/10.1155/2012/237036 |
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