Extremal solutions for nonresonance impulsive functional dynamic equations on time scales

Applied Mathematics and Computation

Volumn 196, Issue 1, 2008, Pages 333-339

  Graef, John R ^a   Ouahab, Abdelghani ^b  

^a UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

^b UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Delta derivative; Extremal solutions; Fixed point; Impulsive functional dynamic equations; Nonresonance; Time scales

Indexed keywords

DIFFERENCE EQUATIONS; FUNCTIONAL ANALYSIS; NUMERICAL METHODS;

DELTA DERIVATIVE; EXTREMAL SOLUTIONS; NONRESONANCE IMPULSIVE FUNCTIONAL DYNAMIC EQUATIONS; PERIODICITY CONDITION; TIME SCALES;

NONLINEAR EQUATIONS;

EID: 38049054058     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.05.056     Document Type: Article

References (25)

1. Agarwal R.P., Benchohra M., O'Regan D., and Ouahab A. Second order impulsive dynamic equations on time scales. Funct. Differ. Equ. 11 (2004) 223-234
2. Agarwal R.P., and Bohner M. Basic calculus on time scales and some of its applications. Res. Math. 35 (1999) 3-22
3. Agarwal R.P., Bohner M., and Wong P.J.Y. Sturm-Liouville eigenvalue problems on time scales. Appl. Math. Comput. 99 (1999) 153-166
4. Agarwal R.P., and O'Regan D. Triple solutions to boundary value problems on time scales. Appl. Math. Lett. 13 (2000) 7-11
5. Anderson D.R. Solutions to second-order three point problems on time scales. J. Differ. Equ. Appl. 8 (2002) 673-688
6. Bainov D.D., and Simeonov P.S. Systems with Impulse Effect (1989), Ellis Horwood Ltd., Chichister
7. Belarbi A., Benchohra M., and Ouahab A. Extremal solutions for impulsive dynamic equations on times scales. Commun. Appl. Nonlinear Anal. 2 (2005) 85-95
8. Benchohra M., and Eloe P. On nonresonance impulsive functional differential equations with periodic boundary conditions. Appl. Math. E-Notes 1 (2001) 65-72
9. Benchohra M., Henderson J., Ntouyas S.K., and Ouahab A. On first order impulsive dynamic equations on time scales. J. Differ. Equ. Appl. 10 (2004) 541-548
10. Benchohra M., Ntouyas S.K., and Ouahab A. Existence results for second order boundary value problem of impulsive dynamic equations on time scales. J. Math. Anal. Appl. 296 (2004) 69-73
11. Bohner M., and Eloe P.W. Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions. J. Math. Anal. Appl. 246 (2000) 639-656
12. Bohner M., and Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser, Boston
13. Bohner M., and Peterson A. Advances in Dynamic Equations on Time Scales (2003), Birkhäuser, Boston
14. Bohner M., and Peterson A. First and second order linear dynamic equations on time scales. J. Differ. Equ. Appl. 7 (2001) 767-792
15. Erbe L., and Peterson A. Positive solutions for nonlinear differential equations on a measure chains. Dynam. Contin. Discrete Impuls. Syst. 6 (1999) 121-137
16. Erbe L., and Peterson A. Green's functions and comparison theorems for differential equations on a measure chains. Math. Comput. Model. 32 (2000) 571-585
17. Graef J.R., and Ouahab A. Nonresonance impulsive functional dynamic equations on times scales. Inter. J. Appl. Math. Sci. 2 (2005) 65-79
18. Heikkila S., and Lakshmikantham V. Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations (1994), Dekker, New York
19. Henderson J. Double solutions of impulsive dynamic boundary value problems on a time scale. J. Differ. Equ. Appl. 8 (2002) 345-356
20. Henderson J., and Tisdell C. Topological transversality and boundary value problems on time scales. J. Math. Anal. Appl. 289 (2003) 110-125
21. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
22. Lakshmikantham V., Sivasundaram S., and Kaymakcalan B. Dynamic Systems on Measure Chains (1996), Kluwer, Dordrecht
23. Nieto J.J. Basic theory for nonresonance impulsive periodic problems of first order. J. Math. Anal. Appl. 205 (1997) 423-433
24. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
25. Sun J.P. A new existence theorem for right focal boundary value problems on a measure chain. Appl. Math. Lett. 18 (2005) 41-47