A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient
A linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solu...
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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/10.1155/2011/586328 |
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| author | J. Baštinec L. Berezansky J. Diblík Z. Šmarda |
| author_facet | J. Baštinec L. Berezansky J. Diblík Z. Šmarda |
| author_sort | J. Baštinec |
| collection | DOAJ |
| description | A linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n→∞. |
| format | Article |
| id | doaj-art-e18e3789df3042eab99929a534f39c32 |
| 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-e18e3789df3042eab99929a534f39c322025-02-03T01:00:57ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/586328586328A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive CoefficientJ. Baštinec0L. Berezansky1J. Diblík2Z. Šmarda3Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicDepartment of Mathematics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, IsraelDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicA linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n→∞.http://dx.doi.org/10.1155/2011/586328 |
| spellingShingle | J. Baštinec L. Berezansky J. Diblík Z. Šmarda A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient Abstract and Applied Analysis |
| title | A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient |
| title_full | A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient |
| title_fullStr | A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient |
| title_full_unstemmed | A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient |
| title_short | A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient |
| title_sort | final result on the oscillation of solutions of the linear discrete delayed equation δx n p n x n k with a positive coefficient |
| url | http://dx.doi.org/10.1155/2011/586328 |
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