Basic results for functional differential and dynamic equations involving impulses

Mathematische Nachrichten

Volumn 286, Issue 2-3, 2013, Pages 181-204

  Federson, Márcia ^a   Mesquita, Jaqueline Godoy ^a   Slavík, Antonín ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Continuous dependence; Existence and uniqueness; Impulsive functional dynamic equations; Impulsive measure functional differential equations; Integration on time scales; Kurzweil Henstock Stieltjes integral; Periodic averaging

Indexed keywords

EID: 84873186646     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.201200006     Document Type: Article

References (16)

1. M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, On first order impulsive dynamic equations on time scales, J. Difference Equ. Appl. 10(6), 541-548 (2004).
2. M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, Impulsive functional dynamic equations on time scales, Dyn. Syst. Appl. 15, 43-52 (2006).
3. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, 2001).
4. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales (Birkhäuser, Boston, 2003).
5. Y. Chang and W. Li, Existence results for impulsive dynamic equations on time scales with nonlocal initial conditions, Math. Comput. Modelling 43, 377-384 (2006).
6. M. Federson, J. G. Mesquita, and A. Slavík, Measure functional differential equations and functional dynamic equations on time scales, J. Differ. Equations 252, 3816-3847 (2012).
7. M. Federson and Š. Schwabik, Generalized ODE approach to impulsive retarded functional differential equations, Differ. Integral Equ. 19(11), 1201-1234 (2006).
8. M. Federson and P. Táboas, Topological dynamics of retarded functional differential equations, J. Differ. Equations 195(2), 313-331 (2003).
9. J. R. Graef and A. Ouahab, Nonresonance impulsive functional dynamic equations on times scales, Int. J. Appl. Math. Sci. 2(1), 65-80 (2005).
10. A. Huseynov, Riesz representation theorem on time scales, Math. Comput. Modelling 55, 1570-1579 (2012).
11. J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czech. Math. J. 7(82), 418-448 (1957).
12. J. G. Mesquita and A. Slavík, Periodic averaging theorems for various types of equations, J. Math. Anal. Appl. 387, 862-877 (2012).
13. D. Mozyrska, E. Pawluszewicz, and D. F. M. Torres, The Riemann-Stieltjes integral on time scales, Aust. J. Math. Anal. Appl. 7, 1-14 (2010).
14. A. Peterson and B. Thompson, Henstock-Kurzweil delta and nabla integrals, J. Math. Anal. Appl. 323, 162-178 (2006).
15. Š. Schwabik, Generalized Ordinary Differential Equations, World Scientific Vol. 5 Series in Real Analysis (1992).
16. A. Slavík, Dynamic equations on time scales and generalized ordinary differential equations, J. Math. Anal. Appl. 385, 534-550 (2012).