In this article, we study the approximate controllability results for an integro-quasilinear evolution equation with random impulsive moments under sufficient conditions. The results are obtained by the theory of C0 semigroup of bounded linear operators on evolution equations and using trajectory reachable sets. Finally, we generalize the results too with and without fixed type impulsive moments.
A. Vinodkumar
,
C. Loganathan
,
S. Vijay
. APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS[J]. Acta mathematica scientia, Series B, 2020
, 40(2)
: 412
-424
.
DOI: 10.1007/s10473-020-0208-4
[1] Abbas S, Bahuguna D. Existence of solutions to quasilinear functional differential equations. Electron J Differ Equ, 2009, 164:1-8
[2] Agarwal R, Hristova S, Donal O'Regan. Exponential stability for differntial equations with random impulses at random times. Advances in Difference Equations, 2013, 2013:372
[3] Anguraj A, Wu S, Vinodkumar A. Existence and Exponential Stability of Semilinear Functional Differential Equations with Random Impulses under Non-uniqueness. Nonlinear Anal TMA, 2011, 74:331-342
[4] Anguraj A, Vinodkumar A. Existence, Uniqueness and Stability Results of Random Impulsive Semilinear Differential Systems. Nonlinear Anal Hybrid Syst, 2010, 4(3):475-483
[5] Balachandran K, Park J Y, Park S H. Controllability of nonlocal impulsive quasilinear integrodifferential systems in Banach spaces. Reports on Math Phys, 2010, 65(2):247-257
[6] Bouzahir Hassane, Fu Xianlong. Controllability of neutral functional differential equations with infinite delay. Acta Mathematica Scientia, 2013, 31B(1):73-80
[7] Debbouchea A, Baleanu D. Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comp Math Appl, 2011, 62:1442-1450
[8] Divya A, Sukavanam N, Shukla A. On the approximate controllability of semilinear control systems. Cogent Mathematics, 2016, 3:1266773
[9] Heard M L. A quasi linear hyperbolic integrodifferential equations related to a nonlinear string. Trans American Math Soc, 1984, 285:805-823
[10] Kato S. Nonhomogeneous quasi-linear evolution equations in Banach spaces. Nonlinear Anal, 1985, 9:1061-1071
[11] Kumar S, Sukavanam N. Approximate controllability of fractional order neutral control systems with delay. I J Nonlinear Sci, 2012, 13:454-462
[12] Lakshmikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations. Singapore:World Scientific, 1989
[13] Naito K. Controllability of semilinear control systems dominated by the linear part. SIAMJ Control Optim, 1987, 25(3):715-722
[14] Naito K, Park J Y. Approximate Controllability for Trajectories of a Delay Volterra Control System. J Optim Ther Appli, 1989, 61:271-279
[15] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York:Springer-Verlag, 1983
[16] Ryu J W, Park J Y, Kwun Y C. Approximate controllability of delay Volterra control system. Bull Korean Math Soc, 1993, 30(2):277-284
[17] Samoilenko A M, Perestyuk N A. Impulsive Differential Equations. Singapore:World Scientific, 1995
[18] Tomar N K, Sukavanam N. Approximate controllability of non-densely defined semilinear delayed control systems. Nonlinear Studies, 2011, 18(2):229-234
[19] Tomar N K, Kumar S. Approximate controllability of nonlocal semilinear time-varying delay control systems. Nonlinear Dynamics and System Theory, 2012, 12(3):303-310
[20] Triggiani R. A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J Control Optim, 1977, 15:407-411
[21] Vinodkumar A, Anguraj A. Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays. Nonlinear Anal Hybrid Syst, 2011, 5:413-426
[22] Anguraj A, Vinodkumar A, Malar K. Existence and Stability Results for Random Impulsive Fractional Pantograph Equations. Filomat, 2016, 30(14):3839-3854
[23] Vinodkumar A, Malar K, Gowrisankar M, Mohankumar P. Existence, uniqueness and stability of random impulsive fractional differential equations. Acta Mathematica Scientia, 2016, 36B(2):428-442
[24] Vijay S, Loganathan C, Vinodkumar A. Approximate controllability of random impulsive semilinear control systems. Nonlinear Studies, 2016, 23(2):273-280
[25] Vinodkumar A, Senthilkumar T, Li X. Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments. Advances in Difference Equations, 2018, 2018(1):39
[26] Harrat A, Nieto Juan J, Debbouche Amar. Solvability and optimal controls of impulsive Hilfer fractional delay evolution inclusions with Clarke subdifferential. Journal of Computational and Applied Mathematics, 2018, 344:725-737
[27] Agarval Ravi P, Dumitru Baleanu, Nieto Juan J, Torres Deifim F M. A survey on fuzzy fractional differential and optimal control nonlocal evolution inclusions. Journal of Computational and Applied Mathematics, 2018, 339:3-29
