Convergence and Divergence of the Solutions of a Neutral Difference Equation
We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ[𝑥(𝑛)+𝑐𝑥(𝜏(𝑛))]+𝑝(𝑛)𝑥(𝜎(𝑛))=0, where 𝜏(𝑛) is a general retarded argument, 𝜎(𝑛) is a general deviated argument (retarded or advanced), 𝑐∈ℝ, (𝑝(𝑛))𝑛≥0 is a sequence of positive real numbers such...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/262316 |
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| author | G. E. Chatzarakis G. N. Miliaras |
| author_facet | G. E. Chatzarakis G. N. Miliaras |
| author_sort | G. E. Chatzarakis |
| collection | DOAJ |
| description | We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ[𝑥(𝑛)+𝑐𝑥(𝜏(𝑛))]+𝑝(𝑛)𝑥(𝜎(𝑛))=0, where 𝜏(𝑛) is a general retarded argument, 𝜎(𝑛) is a general deviated argument (retarded or advanced), 𝑐∈ℝ, (𝑝(𝑛))𝑛≥0 is a sequence of positive real numbers such that 𝑝(𝑛)≥𝑝, 𝑝∈ℝ+, and Δ denotes the forward difference operator Δ𝑥(𝑛)=𝑥(𝑛+1)−𝑥(𝑛). Also, we examine the asymptotic behavior of the solutions in case they are
continuous and differentiable with respect to 𝑐. |
| format | Article |
| id | doaj-art-a6f70db716b44b16a4efc53e090cd98e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a6f70db716b44b16a4efc53e090cd98e2025-08-20T03:38:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/262316262316Convergence and Divergence of the Solutions of a Neutral Difference EquationG. E. Chatzarakis0G. N. Miliaras1Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, GreeceDepartment of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, GreeceWe investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ[𝑥(𝑛)+𝑐𝑥(𝜏(𝑛))]+𝑝(𝑛)𝑥(𝜎(𝑛))=0, where 𝜏(𝑛) is a general retarded argument, 𝜎(𝑛) is a general deviated argument (retarded or advanced), 𝑐∈ℝ, (𝑝(𝑛))𝑛≥0 is a sequence of positive real numbers such that 𝑝(𝑛)≥𝑝, 𝑝∈ℝ+, and Δ denotes the forward difference operator Δ𝑥(𝑛)=𝑥(𝑛+1)−𝑥(𝑛). Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to 𝑐.http://dx.doi.org/10.1155/2011/262316 |
| spellingShingle | G. E. Chatzarakis G. N. Miliaras Convergence and Divergence of the Solutions of a Neutral Difference Equation Journal of Applied Mathematics |
| title | Convergence and Divergence of the Solutions of a Neutral Difference Equation |
| title_full | Convergence and Divergence of the Solutions of a Neutral Difference Equation |
| title_fullStr | Convergence and Divergence of the Solutions of a Neutral Difference Equation |
| title_full_unstemmed | Convergence and Divergence of the Solutions of a Neutral Difference Equation |
| title_short | Convergence and Divergence of the Solutions of a Neutral Difference Equation |
| title_sort | convergence and divergence of the solutions of a neutral difference equation |
| url | http://dx.doi.org/10.1155/2011/262316 |
| work_keys_str_mv | AT gechatzarakis convergenceanddivergenceofthesolutionsofaneutraldifferenceequation AT gnmiliaras convergenceanddivergenceofthesolutionsofaneutraldifferenceequation |