Density Problems in Sobolev’s Spaces on Time Scales

Download PDF


DOI: 10.46793/KgJMat2102.215C


In this paper, we present a generalization of the density some of the functional spaces on the time scale, for example, spaces of rd-continuous function, spaces of Lebesgue Δ-integral and first-order Sobolev’s spaces.


Time scale, Lebesgue’s spaces, Sobolev’s spaces.


[1]   M. Bohner and A. C.Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkäuser Boston, Boston, 2001.

[2]   M. Bohner and A. C. Peterson, Advances in Dynamic Equations on Time Scales, Birkäuser Boston, Boston, 2003.

[3]   A. Cabada and D. Vivero, Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral, application to the calculus of Δ-antiderivatives, Math. Comput. Modelling 43 (2006), 194–207.

[4]   S. Hilger, Ein Maβkettenakalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. Thesis, Universität Würzburg, 1988 (in German).

[5]   V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Boston, 1996.

[6]   H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1996.

[7]   R. B. Agarwal, V. O. Espinar, K. Perera and D. R. Vivero, Basic properties of Sobolev’s spaces on time scales, Adv. Difference Equ. (2006), 1–14.

[8]   A. Benaissa Cherif, A. Hammoudi and F. Z. Ladrani, Density problems in LpΔ(????, ℝ ) space, Electronic Journal of Mathematical Analysis and Applications 1(2) (2013), 178–187.

[9]   Y. H. Sua and Z. Fengb, Variational approach for a p-Laplacian boundary value problem on time scales, Appl. Anal. 97(13) (2017), DOI 10.1080/00036811.2017.1359566.