Time scales: from Nabla calculus to Delta calculus and vice versa via duality

Preprint English OPEN
Caputo, M. Cristina;
(2009)
  • Subject: Mathematics - Optimization and Control | Mathematics - Classical Analysis and ODEs | 39A10, 26E70, 49K05
    arxiv: Computer Science::Logic in Computer Science

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.
  • References (10)

    [3] F. M. Atici, C.S. McMahan A Comparison in the Theory of Calculus of Variations on Time Scales with an Application to the Ramsey Model Nonlinear Dynamics and Systems Theory, 9 (1) (2009) 1-10.

    [4] M. Bohner Calculus of variations on time scales Dynam. Systems Appl. 13 (34) (2004), 339-349.

    [5] M. Bohner, A. Peterson Dynamic equations on time scales: an introduction with applications Birkhauser, Boston, Base, Berlin, (2001).

    [6] R. A. C. Ferreira, D. F. M. Torres Remarks on the calculus of variations on time scales Int. J. Ecol. Econ. Stat. 9 (2007), no. F07, 65-73.

    [7] R. A. C. Ferreira, D. F. M. Torres Higher-order calculus of variations on time scales Mathematical control theory and finance, Springer, Berlin, (2008), 149- 159.

    [8] M. G u¨rses, G. S. Guseinov, B. Silindir Integrable equations on time scales J. Math. Phys. 46 no. (11), 113510, (2005), 22 pp.

    [9] S. Hilger Ein Makettenkalkl mit Anwendung auf Zentrumsmannigfaltigkeiten Ph.D. Thesis, Universtat Wurzburg, 1988.

    [10] R. Hilscher, V. Zeidan Calculus of variations on time scales: Weak local piecewise Cr1d solutions with variable endpoints J. Math. Anal. Appl. 289 (1) (2004), 143- 166.

    [11] A. B. Malinowska, D.F. M. Torres Strong minimizers of the calculus of variations on time scales and the Weierstrass condition Proceedings of the Estonian Academy of Sciences, Vol. 58, no. 4, 2009, 205-212.

    [12] N. Martins, D. F. M. Torres Calculus of variations on time scales with nabla derivatives Nonlinear Analysis Series A: Theory, Methods & Applications, 71 (2009), no. 12, pp. e763-e773.

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