Artículo
Amster, P.; De Napoli, P.; Pinasco, J.P. "Detailed asymptotic of eigenvalues on time scales" (2009) Journal of Difference Equations and Applications. 15(3):225-231
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Abstract:
Let ={an}n{0} be a time scale with zero Minkowski (or box) dimension, where {an}n is a monotonically decreasing sequence converging to zero, and a1=1. In this paper, we find an upper bound for the eigenvalue counting function of the linear problem -u=u, with Dirichlet boundary conditions. We obtain that the nth-eigenvalue is bounded below by [image omitted]. We show that the bound is optimal for the q-difference equations arising in quantum calculus.
Registro:
| Documento: | Artículo |
| Título: | Detailed asymptotic of eigenvalues on time scales |
| Autor: | Amster, P.; De Napoli, P.; Pinasco, J.P. |
| Filiación: | Departamento de Matematica, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Argentina Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, Los Polvorines, 1613 Provincia de Buenos Aires, Argentina |
| Palabras clave: | Asymptotic bounds; Asymptotic of eigenvalues; Minkowski dimension; Time scales |
| Año: | 2009 |
| Volumen: | 15 |
| Número: | 3 |
| Página de inicio: | 225 |
| Página de fin: | 231 |
| DOI: | http://dx.doi.org/10.1080/10236190802040976 |
| Título revista: | Journal of Difference Equations and Applications |
| Título revista abreviado: | J. Differ. Equ. Appl. |
| ISSN: | 10236198 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10236198_v15_n3_p225_Amster |
Referencias:
- Agarwal, R.P., Bohner, M., Basic calculus on time scales and some of its applications (1999) Results Math, 35 (1-2), pp. 3-22
- Agarwal, R.P., Bohner, M., Wong, P.J.Y., Sturm-Liouville eigenvalue problems on time scales (1999) Appl. Math. Comput, 99 (2-3), pp. 153-166
- Amster, P., De Napoli, P., Pinasco, J.P., Eigenvalue distribution of second-order dynamic equations on time scales considered as fractals Journal of Mathematical Analysis and Applications, , http://dx.doi.org/10.1016/j.jmaa.2008.01.070, To appear in
- Bohner, M., Hudson, T., Euler-type boundary value problems in quantum calculus (2007) Int. J. Appl. Math. Stat, 9, pp. 19-23
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- Davidson, F.A., Rynne, B.P., Eigenfunction expansions in L 2 spaces for boundary value problems on time scales (2007) J. Math. Anal. Appl, 335, pp. 1038-1051
- Ernst, T., (2001) The history of q-calculus and a new method, , www.math.uu.se/research/pub/Ernst4.pdf, Thesis, Department of Mathematics, Uppsala University. Available at
- Falconer, K., (2003) Fractal Geometry, Mathematical Foundations and Applications, , 2nd ed, John Wiley, New York
- Guseinov, G.S., Kaymakcalan, B., On a disconjugacy criterion for second order dynamic equations on time scales (2002) J. Comput. Appl. Math, 141, pp. 187-196
- Kac, V., Cheung, P., (2002) Quantum Calculus, , Universitext Springer-Verlag, New York
Citas:
---------- APA ----------
Amster, P., De Napoli, P. & Pinasco, J.P. (2009) . Detailed asymptotic of eigenvalues on time scales. Journal of Difference Equations and Applications, 15(3), 225-231.http://dx.doi.org/10.1080/10236190802040976
---------- CHICAGO ----------
Amster, P., De Napoli, P., Pinasco, J.P. "Detailed asymptotic of eigenvalues on time scales" . Journal of Difference Equations and Applications 15, no. 3 (2009) : 225-231.http://dx.doi.org/10.1080/10236190802040976
---------- MLA ----------
Amster, P., De Napoli, P., Pinasco, J.P. "Detailed asymptotic of eigenvalues on time scales" . Journal of Difference Equations and Applications, vol. 15, no. 3, 2009, pp. 225-231.http://dx.doi.org/10.1080/10236190802040976
---------- VANCOUVER ----------
Amster, P., De Napoli, P., Pinasco, J.P. Detailed asymptotic of eigenvalues on time scales. J. Differ. Equ. Appl. 2009;15(3):225-231.http://dx.doi.org/10.1080/10236190802040976
