Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001),...
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2769 |
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| author | Anna Kisiolek Ireneusz Kubiaczyk |
| author_facet | Anna Kisiolek Ireneusz Kubiaczyk |
| author_sort | Anna Kisiolek |
| collection | DOAJ |
| description | We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness. |
| format | Article |
| id | doaj-art-d430b300755440a68b0b9cab47ca5598 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d430b300755440a68b0b9cab47ca55982025-02-03T05:59:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005172769277410.1155/IJMMS.2005.2769Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spacesAnna Kisiolek0Ireneusz Kubiaczyk1Institute of Mathematics, Poznan University of Technology, 5 Maria Sklodowska-Curie Square, Poznan 60-965, PolandCollegium Mathematicum, Adam Mickiewicz University, Umultowska 87, Poznan 61-614, PolandWe consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.http://dx.doi.org/10.1155/IJMMS.2005.2769 |
| spellingShingle | Anna Kisiolek Ireneusz Kubiaczyk Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces |
| title_full | Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces |
| title_fullStr | Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces |
| title_full_unstemmed | Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces |
| title_short | Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces |
| title_sort | asymptotic behaviour of solutions of nonlinear delay difference equations in banach spaces |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2769 |
| work_keys_str_mv | AT annakisiolek asymptoticbehaviourofsolutionsofnonlineardelaydifferenceequationsinbanachspaces AT ireneuszkubiaczyk asymptoticbehaviourofsolutionsofnonlineardelaydifferenceequationsinbanachspaces |