A class of the first order impulsive dynamic equations on time scales

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 9, 2008, Pages 2803-2811

  Liu, Hongbo ^a   Xiang, X ^a  

^a GUIZHOU UNIVERSITY   (China)

Author keywords

Delta derivative; Fixed point; Gronwall's inequality; Impulsive differential equation; Measure chains; Time scales

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; TIME MEASUREMENT;

DELTA DERIVATIVES; FIXED POINTS; GRONWALL'S INEQUALITY; IMPULSIVE DIFFERENTIAL EQUATION; MEASURE CHAIN; TIME-SCALES;

NONLINEAR EQUATIONS;

EID: 64849114317     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.08.052     Document Type: Article

References (24)

1. B. Aulbach, S. Hilger, Linear dynamical processes with inhomogeneous time scale, in: Nonlinear Dynamics and Quantum Dynamical Systems, Akademie Verlag, Berlin, 1990.
2. D.R. Anderson, Eigenvalue intervals for a second-order mixed-conditions problem on time scales, Int. J. Nonlin. Differential Equations 7 (2002) 97-104.
3. D.R. Anderson, Eigenvalue intervals for a two-point boundary value problem on a measure chain, J. Comput. Appl. Math. 141 (2002) 57-64.
4. D.R. Anderson, Solutions to second-order three point problems on time scales, J. Difference Equ. Appl. 8 (2002) 673-688.
5. F.M. Aticia, A. Cabadab, C.J. Chyanc, B. Kaymakcaland, Nagumo type existence results for second-order nonlinear dynamic BVPS, Nonlinear Anal. 60 (2005) 209-220.
6. J. Henderson, Double solutions of impulsive dynamic boundary value problems on a time scale, J. Difference Equ. Appl. 8 (2002) 345-356.
7. L. Erbe, A. Peterson, Green's functions and comparison theorems for differential equations on a measure chain, Math. Comput. Modelling 32 (2000) 571-585.
8. L. Erbe, A. Peterson, Positive solutions for nonlinear differential equations on a measure chain, Dyn. Contin. Discrete Impuls. Syst. 6 (1999) 121-137.
9. M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, On first order impulsive dynamic equations on time scales, J. Difference Equ. Appl. 10 (2004) 541-548.
10. M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
11. M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
12. M. Bohner, A. Peterson, First and second order linear dynamic equations on time scales, J. Difference Equ. Appl. 7 (2001) 767-792.
13. M. Bohner, G.Sh. Guseinov, Improper integrals on time scales, Dynam. Systems Appl. 12 (2003) 45-65.
14. M. Bohner, P.W. Eloe, Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions, J. Math. Anal. Appl. 246 (2000) 639-656.
15. N.U. Ahmed, Optimal impulsive control for impulsive systems in banach spaces, Int. J. Differ. Equ. Appl. 1.1 (2002) 37-52.
16. R. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: A survey, Math. Inequal. Appl. 4 (4) (2001) 535-557.
17. R.P. Agarwal, D. O'Regan, Infinite Interval Problems for Differential Difference and Integral Equations, Kluwer Acad. Pub., Dordrecht, 2001.
18. R.P. Agarwal, D. O'Regan, Triple solutions to boundary value problems on time scales, Appl. Math. Lett. 13 (2000) 7-11.
19. R.P. Agarwal, M. Bohner, P.J.Y. Wong, Sturm-Liouville eigenvalue problems on time scales, Appl. Math. Comput. 99 (1999) 153-166.
20. R.P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35 (1999) 3-22.
21. R.P. Agarwal, M. Bohner, Quadratic functionals for second-order matrix equations on time scales, Nonlinear Anal. 33 (1998) 675-692.
22. V. Lakshmikantham, S. Sivasundaram, B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
23. Wei Wei, X. Xiang, Optimal control for a class of strongly nonlinear impulsive equations in Banach spaces, Nonlinear Anal. 63 (5-7) (2005) e53-e63.
24. X. Xiang, W. Wei, Y. Jiang, Strongly nonlinear impulsive system and necessary conditions of optimality, Dyn. Contin. Discrete Impuls. Syst. 12 (6) (2005) 811-824.