Asymptotic behavior of solutions of difference equations in Banach spaces
HTML articles powered by AMS MathViewer
- by Cristóbal González and Antonio Jiménez-Melado PDF
- Proc. Amer. Math. Soc. 128 (2000), 1743-1749 Request permission
Abstract:
In this paper we consider the first order difference equation \[ \Delta x_n = \sum _{i=0}^\infty a_n^i f(x_{n+i}), \] and give necessary and sufficient conditions so that there exist solutions which are asymptotically constant. These results generalize those given earlier by Popenda and Schmeidel. As an application we give necessary and sufficient conditions for the second order difference equation \[ \Delta (q_n \Delta x_n) + p_n f(x_n) =0 \] to have asymptotically constant solutions.References
- Andrzej Drozdowicz and Jerzy Popenda, Asymptotic behavior of the solutions of the second order difference equation, Proc. Amer. Math. Soc. 99 (1987), no. 1, 135–140. MR 866443, DOI 10.1090/S0002-9939-1987-0866443-0
- P. K. Lin and Y. Sternfeld, Convex sets with the Lipschitz fixed point property are compact, Proc. Amer. Math. Soc. 93 (1985), no. 4, 633–639. MR 776193, DOI 10.1090/S0002-9939-1985-0776193-5
- Jerzy Popenda and Ewa Schmeidel, On the asymptotic behavior of solutions of linear difference equations, Publ. Mat. 38 (1994), no. 1, 3–9. MR 1291948, DOI 10.5565/PUBLMAT_{3}8194_{0}1
- Ewa Schmeidel, On the asymptotic behaviour of solutions of difference equations, Demonstratio Math. 30 (1997), no. 1, 193–197. MR 1446611
Additional Information
- Cristóbal González
- Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, Fac. Ciencias, 29071 Málaga, Spain
- Email: gonzalez@anamat.cie.uma.es
- Antonio Jiménez-Melado
- Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, Fac. Ciencias, 29071 Málaga, Spain
- Email: jimenez@anamat.cie.uma.es
- Received by editor(s): July 21, 1998
- Published electronically: February 3, 2000
- Additional Notes: This research was partially supported by a grant from Ministerio de Educación y Cultura (Spain) PB97-1081, and from La Junta de Andalucía
- Communicated by: Hal L. Smith
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1743-1749
- MSC (1991): Primary 39A10; Secondary 47N99
- DOI: https://doi.org/10.1090/S0002-9939-00-05490-3
- MathSciNet review: 1695135