Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a mea...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/2368694 |
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| author | Janusz Migda Małgorzata Migda Magdalena Nockowska-Rosiak |
| author_facet | Janusz Migda Małgorzata Migda Magdalena Nockowska-Rosiak |
| author_sort | Janusz Migda |
| collection | DOAJ |
| description | We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation. |
| format | Article |
| id | doaj-art-99c04747b3884cd091b8714a1c160598 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-99c04747b3884cd091b8714a1c1605982025-02-03T01:30:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/23686942368694Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra TypeJanusz Migda0Małgorzata Migda1Magdalena Nockowska-Rosiak2Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, PolandInstitute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, PolandInstitute of Mathematics, Lodz University of Technology, Ul. Wólczańska 215, 90-924 Łódź, PolandWe consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation.http://dx.doi.org/10.1155/2018/2368694 |
| spellingShingle | Janusz Migda Małgorzata Migda Magdalena Nockowska-Rosiak Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type Discrete Dynamics in Nature and Society |
| title | Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type |
| title_full | Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type |
| title_fullStr | Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type |
| title_full_unstemmed | Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type |
| title_short | Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type |
| title_sort | asymptotic properties of solutions to second order difference equations of volterra type |
| url | http://dx.doi.org/10.1155/2018/2368694 |
| work_keys_str_mv | AT januszmigda asymptoticpropertiesofsolutionstosecondorderdifferenceequationsofvolterratype AT małgorzatamigda asymptoticpropertiesofsolutionstosecondorderdifferenceequationsofvolterratype AT magdalenanockowskarosiak asymptoticpropertiesofsolutionstosecondorderdifferenceequationsofvolterratype |