Citation: Yanfang Li, Yanmin Liu, Xianghu Liu, He Jun. On the approximate controllability for some impulsive fractional evolution hemivariational inequalities[J]. AIMS Mathematics, 2017, 2(3): 422-436. doi: 10.3934/Math.2017.3.422
| [1] | A.E. Bashirov and N.I. Mahmudov, On concepts of controllability for deterministic and stochastic systems, SIAM J. Control Optim, 37 (1999), 1808-1821. |
| [2] | H. F. Bohnenblust and S. Karlin, On a Theorem of Ville, in: Contributions to the Theory of Games, Princeton University Press, Princeton, NJ, 1950,155-160. |
| [3] | P. Cannarsa, G. Fragnelli, and D. Rocchetti, Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form, J. Evol. Equ., 8 (2008), 583-616. |
| [4] | S. Carl and D. Motreanu, Extremal solutions of quasilinear parabolic inclusions with generalized Clarke0s gradient, J. Differ. Equa., 191 (2003), 206-233. |
| [5] | F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. |
| [6] | Z. Denkowski, S. Migórski, and N.S. Papageorgiou, An Introduction to Non-linear Analysis: Theory, Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. |
| [7] | S. Hu and N.S. Papageorgiou, Handbook of multivalued Analysis (Theory), Kluwer Academic Publishers, Dordrecht Boston, London, 1997. |
| [8] | A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Studies, Elservier Science B. V. Amsterdam, 204,2006. |
| [9] | M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991. |
| [10] | A. Kulig, Nonlinear evolution inclusions and hemivariational inequalities for nonsmooth problems in contact mechanics. PhD thesis, Jagiellonian University, Krakow, Poland, 2010. |
| [11] | S. Kumar and N. Sukavanam, Approximate controllability of fractional order semilinear systems with bounded delay, J. Differ. Equa., 252 (2012), 6163-6174. |
| [12] | Z.H. Liu, A class of evolution hemivariational inequalities, Nonlinear Anal. Theory Methods Appl., 36 (1999), 91-100. |
| [13] | Z.H. Liu, Anti-periodic solutions to nonlinear evolution equations, J. Funct. Anal., 258 (2010), 2026-2033. |
| [14] | Z.H. Liu and X.W. Li, Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat., 18 (2013), 1362-1373. |
| [15] | Z.H. Liu and X.W. Li, On the Controllability of Impulsive Fractional Evolution Inclusions in Banach Spaces, J. Optim. Theory Appl., 156 (2013), 167-182. |
| [16] | Z.H. Liu and J.Y. Lv, R. Sakthivel, Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces, IMA. J. Math. Control Info., 31 (2014), 363-383. |
| [17] | N.I. Mahmudov, Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces, SIMA. J. Control Optim., 42 (2003), 1604-1622. |
| [18] | S. Migórski and A. Ochal, Existence of solutions for second order evolution inclusions with application to mechanical contact problems, Optimization, 55 (2006), 101-120. |
| [19] | S. Migórski and A. Ochal, Quasi-static hemivariational inequality via vanishing acceleration approach, SIAM J. Math. Anal., 41 (2009), 1415-1435. |
| [20] | S. Migórski, A. Ochal, and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics, Springer, New York, 26,2013. |
| [21] | S. Migorski, Existence of Solutions to Nonlinear Second Order Evolution Inclusions without and with Impulses, Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 18 (2011), 493-520. |
| [22] | S. Migorski and A. Ochal, Nonlinear Impulsive Evolution Inclusions of Second Order, Dynam. Syst. Appl., 16 (2007), 155-174. |
| [23] | P.D. Panagiotopoulos, Nonconvex superpotentials in sense of F.H. Clarke and applications, Mech. Res. Comm., 8 (1981), 335-340. |
| [24] | P. D. Panagiotopoulos, Hemivariational inequalities, Applications in Mechanics and Engineering, Springer, Berlin, 1993. |
| [25] | P. D. Panagiotopoulos, Hemivariational inequality and Fan-variational inequality, New Applications and Results, Atti. Sem. Mat. Fis. Univ. Modena XLⅢ, (1995), 159-191. |
| [26] | I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. |
| [27] | K. Rykaczewski, Approximate conrtollability of differential inclusions in Hilbert spaces, Nonlinear Analysis, 75 (2012), 2701-2712. |
| [28] | Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Compu. Math. Appl., 59 (2010), 1063-1077. |
| [29] | E. Zuazua, Controllability of a system of linear thermoelasticity, J. Math. Pures Appl., 74 (1995), 291-315. |
| [30] | Jinrong Wang, M. Fe${\tilde c}$ckan, and Y. Zhou, On the new concept of solutions and existence results for impulsive fractional evolution equations, Dynamics of PDE, 8 (2011), 345-361. |
Yanfang Li, Yanmin Liu, Xianghu Liu, He Jun. On the approximate controllability for some impulsive fractional evolution hemivariational inequalities[J]. AIMS Mathematics, 2017, 2(3): 422-436. doi: 10.3934/Math.2017.3.422
DownLoad: