On controllability of second order nonlinear impulsive differential systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 1-2, 2009, Pages 45-52

  Sakthivel, R ^a   Mahmudov, N I ^b   Kim, J H ^c  

^a Sungkyunkwan University   (South Korea)

^b EASTERN MEDITERRANEAN UNIVERSITY   (Turkey)

^c Yonsei University   (South Korea)

Author keywords

Controllability; Fixed point theorem; Nonlinear impulsive systems; Nonlocal conditions

Indexed keywords

COMPACTNESS CONDITIONS; COSINE FAMILIES; DIFFERENTIAL SYSTEMS; DYNAMICAL BEHAVIORS; DYNAMICAL PROCESS; ENGINEERING SCIENCE; EXACT CONTROLLABILITIES; FIXED POINT THEOREM; FIXED-POINT ANALYSIS; IMPULSE EFFECTS; IMPULSIVE CONTROLS; NONLINEAR IMPULSIVE DIFFERENTIAL SYSTEMS; NONLINEAR IMPULSIVE SYSTEMS; NONLOCAL CONDITIONS; SECOND ORDERS; SUFFICIENT CONDITIONS;

CONTROLLABILITY; MATHEMATICAL OPERATORS;

DYNAMICAL SYSTEMS;

EID: 67349262331     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.10.029     Document Type: Article

References (27)

1. Byszewski L. Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. Journal of Mathematical Analysis and Applications 162 (1991) 494-505
2. Benchohra M., and Ouahab A. Controllability results for functional semilinear differential inclusions in Frechet spaces. Nonlinear Analysis 61 (2005) 405-423
3. Benchohra M., Gorniewicz L., Ntouyas S.K., and Ouahab A. Controllability results for impulsive functional differential inclusions. Reports on Mathematical Physics 54 (2004) 211-228
4. Benchohra M., and Ntouyas S.K. Controllability of second order differential inclusion in Banach spaces with nonlocal conditions. Journal of Optimization Theory and Applications 107 (2000) 559-571
5. Bashirov A.E., and Mahmudov N.I. On concepts of controllability for deterministic and stochastic systems. SIAM Journal on Control and Optimization 37 (1999) 1808-1821
6. Chang Y.K., Li W.T., and Nieto J.J. Controllability of evolution differential inclusions in Banach spaces. Nonlinear Analysis 67 (2007) 623-632
7. Chang Y.K., and Li W.T. Controllability of second order differential and integrodifferential inclusions in Banach spaces. Journal of Optimization Theory and Applications 129 (2006) 77-87
8. Chang Y.K. Controllability of impulsive functional differential systems with infinite delay in Banach spaces. Chaos, Solitons & Fractals 33 (2007) 1601-1609
9. Dauer J.P., and Mahmudov N.I. Controllability of some nonlinear systems in Hilbert spaces. Journal of Optimization Theory and Applications 123 (2004) 319-329
10. Fattorini H.O. Second order linear differential equations in Banach spaces. North Holland Mathematics Studies vol. 108 (1985), Elsevier Science, North Holland
11. Fitzgibbon W.E. Global existence and boundedness of solutions to the extensible beam equation. SIAM Journal of Mathematical Analysis 13 (1982) 739-745
12. Gorniewicz L., Ntouyas S.K., and Regan D.O. Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces. Reports on Mathematical Physics 56 (2005) 437-470
13. Gorniewicz L., Ntouyas S.K., and Regan D.O. Existence and controllability results for first- and second-order functional semilinear differential inclusions with nonlocal conditions. Numerical Functional Analysis and Optimization 28 (2007) 53-82
14. George R.K., Chalishajar D.N., and Nandakumaran A.K. Controllability of second order semilinear neutral functional differential inclusions in Banach spaces. Mediterranean Journal of Mathematics 1 (2004) 463-477
15. Hernandez E.M., and Pelicer L.M. Existence results for a second-order abstract Cauchy problem with nonlocal conditions. Electronic Journal of Differential Equations 73 (2005) 1-17
16. Kouemou-Patcheu S. On a global solution and asymptotic behaviour for the generalized damped extensible beam equation. Journal of Differential Equations 135 (1997) 299-314
17. Liu B. Controllability of impulsive neutral functional differential inclusions with infinite delay. Nonlinear Analysis 60 (2005) 1533-1552
18. Li M.L., Wang M.S., and Zhang F.Q. Controllability of impulsive functional differential systems in Banach spaces. Chaos, Solitons & Fractals 29 (2006) 175-181
19. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
20. Mahmudov N.I., and Mckibben M.A. Approximate controllability of second order neutral stochastic evolution equations. Dynamics of Continuous, Discrete and Impulsive Systems 13 (2006) 619-634
21. Mahmudov N.I. Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM Journal on Control and Optimization 42 (2003) 1604-1622
22. Sakthivel R., Anthoni S.M., and Kim J.H. Existence and controllability result for semilinear evolution integrodifferential systems. Mathematical and Computer Modelling 41 (2005) 1005-1011
23. Sakthivel R., Choi Q.H., and Anthoni S.M. Controllability result for nonlinear evolution integrodifferential systems. Applied Mathematics Letters 17 (2004) 1015-1023
24. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
25. Travis C.C., and Webb G.F. Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston Journal of Mathematics 3 (1977) 555-567
26. Travis C.C., and Webb G.F. Cosine families and abstract nonlinear second order differential equations. Acta Mathematica Academia Scientia Hungaricae 32 (1978) 76-96
27. Yang T. Impulsive Systems and Control: Theory and Applications (2001), Springer-Verlag, Berlin, Germany