Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations
We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj), i=0,1,2,…, where fj(x) (j=0,…,i) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/867623 |
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| _version_ | 1849308251596783616 |
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| author | E. Messina Y. Muroya E. Russo A. Vecchio |
| author_facet | E. Messina Y. Muroya E. Russo A. Vecchio |
| author_sort | E. Messina |
| collection | DOAJ |
| description | We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj), i=0,1,2,…, where fj(x) (j=0,…,i) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations. |
| format | Article |
| id | doaj-art-146c5997805c4eb4bef558e8f52cddbe |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-146c5997805c4eb4bef558e8f52cddbe2025-08-20T03:54:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/867623867623Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete EquationsE. Messina0Y. Muroya1E. Russo2A. Vecchio3Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, ItalyDepartment of Mathematics, Waseda University, 3-4-1 Ohkubo Shinjuku-ku, Tokyo 169-8555, JapanDipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, ItalyIstituto per le Applicazioni del Calcolo “Mauro Picone”, Sede di Napoli, Via P. Castellino 111, 80131 Napoli, ItalyWe consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj), i=0,1,2,…, where fj(x) (j=0,…,i) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.http://dx.doi.org/10.1155/2008/867623 |
| spellingShingle | E. Messina Y. Muroya E. Russo A. Vecchio Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations Discrete Dynamics in Nature and Society |
| title | Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations |
| title_full | Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations |
| title_fullStr | Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations |
| title_full_unstemmed | Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations |
| title_short | Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations |
| title_sort | asymptotic behavior of solutions for nonlinear volterra discrete equations |
| url | http://dx.doi.org/10.1155/2008/867623 |
| work_keys_str_mv | AT emessina asymptoticbehaviorofsolutionsfornonlinearvolterradiscreteequations AT ymuroya asymptoticbehaviorofsolutionsfornonlinearvolterradiscreteequations AT erusso asymptoticbehaviorofsolutionsfornonlinearvolterradiscreteequations AT avecchio asymptoticbehaviorofsolutionsfornonlinearvolterradiscreteequations |