Solvability of a Second Order Nonlinear Neutral Delay Difference Equation
This paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillator...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/328914 |
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| _version_ | 1832545649973788672 |
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| author | Zeqing Liu Liangshi Zhao Jeong Sheok Ume Shin Min Kang |
| author_facet | Zeqing Liu Liangshi Zhao Jeong Sheok Ume Shin Min Kang |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | This paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence
results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation,
respectively. Ten examples are given to illustrate the results presented in this paper. |
| format | Article |
| id | doaj-art-72e2558731414a0783630131099ab839 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-72e2558731414a0783630131099ab8392025-02-03T07:25:08ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/328914328914Solvability of a Second Order Nonlinear Neutral Delay Difference EquationZeqing Liu0Liangshi Zhao1Jeong Sheok Ume2Shin Min Kang3Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Changwon National University, Changwon 641-773, Republic of KoreaDepartment of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of KoreaThis paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation, respectively. Ten examples are given to illustrate the results presented in this paper.http://dx.doi.org/10.1155/2011/328914 |
| spellingShingle | Zeqing Liu Liangshi Zhao Jeong Sheok Ume Shin Min Kang Solvability of a Second Order Nonlinear Neutral Delay Difference Equation Abstract and Applied Analysis |
| title | Solvability of a Second Order Nonlinear Neutral Delay Difference Equation |
| title_full | Solvability of a Second Order Nonlinear Neutral Delay Difference Equation |
| title_fullStr | Solvability of a Second Order Nonlinear Neutral Delay Difference Equation |
| title_full_unstemmed | Solvability of a Second Order Nonlinear Neutral Delay Difference Equation |
| title_short | Solvability of a Second Order Nonlinear Neutral Delay Difference Equation |
| title_sort | solvability of a second order nonlinear neutral delay difference equation |
| url | http://dx.doi.org/10.1155/2011/328914 |
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