Một lớp bất đẳng thức hemivariational phân cấp Hilfer với các toán tử phụ thuộc vào lịch sử

Bin, M.J., Deng, H.Y., Li, Y.X., Zhao, J.: Properties of the set of admissible state control pair for a class of fractional semilinear evolution control systems. Fract. Calc. Appl. Anal. 24(2), 1275–1298 (2021). DOI: 10.1515/fca-2021-0055 Anh, N.T.V., Ke, T.D.: On the differential variational inequalities of parabolic-parabolic type. Acta Applicandae Mathematicae 176(5), 1–25 (2021) Bohnenblust, H.F., Karlin, S.: On a theorem of Ville, in: Contributions to the Theory of Games. Princeton University Press, Princeton, New Jersey (1950) Browder, F.E., Hess, P.: Nonlinear mappings of monotone type in Banach spaces. J. Funct. Anal. 11, 251–294 (1972) Chen, X., Wang, Z.: Convergence of regularized time-stepping methods for differential variational inequalities. SIAM J. Optim. 23, 1647–1671 (2013) Chen, X., Wang, Z.: Differential variational inequality approach to dynamic games with shared constraints. Math. Program. 146, 379–408 (2014) Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, Interscience, New York (1983) Denkowski, Z., Migórski, S., Papageorgiou, N.S.: An Introduction to Nonlinear Analysis: Theory. Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York (2003) Giannessi, F., Khan, A.A.: Regularization of non-coercive quasi variational inequalities. Control and Cybernetics 29(1), 91–110 (2000) Gu, H., Trujillo, J.J.: Existence of mild solution for evolution equation with Hilfer fractional derivative. Applied Mathematics and Computation 257(15), 344–354 (2015) Gwinner, J.: On a new class of differential variational inequalities and a stability result. Math. Program. 139, 205–221 (2013) Han, L., Pang, J.S.: Non-zenoness of a class of differential quasi-variational inequalities. Math. Program. 121, 171–199 (2010) Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific (2000) Hu, S., Papageorgiou, N.S.: Handbook of Multivalued Analysis, Vol. I: Theory. Kluwer, Dordrecht, Netherlands (1997) Kamenskii, M., Obukhovskii, V., Zecca, P.: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space. Walter de Gruyter, Berlin (2001) Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies (2006) Li, X.W., Liu, Z.H.: Sensitivity analysis of optimal control problems described by differential hemivariational inequalities. SIAM J. Comtrol Optim. 56(5), 3569–3597 (2018) Li, X.W., Liu, Z.H., Li, J., Tisdell, C. C.: Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces. Acta Mathematica Scientia 39(1), 229–242 (2019) Li, X.W., Li, Y.X., Liu, Z.H., Li, J.: Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions. Fract. Calc. Appl. Anal. 21(6), 1439–1470 (2018). DOI: 10.1515/fca-2018-0076 Li, X.W., Liu, Z.H., Papageorgiou, N.S.: Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications. Nonlinearity 36, 1323–1348 (2023) Liu, Y.J., Liu, Z.H., Peng, S., Wen, C.F.: Optimal feedback control for a class of fractional evolution equations with history-dependent operators. Fract. Calc. Appl. Anal. 25, 1108–1130 (2022). DOI: 10.1007/s13540-022-00054-y Liu, Y.J., Liu, Z.H., Papageorgiou, N.S.: Sensitivity analysis of optimal control problems driven by dynamic history-dependent variational- hemivariational inequalities. Journal of Differential Equations 342, 559–595 (2023) Liu, Y.J., Liu, Z.H., Wen, C.F.: Existence of solutions for space-fractional parabolic hemivariational inequalities. Discrete and Continuous Dynamical Systems Series B 24(3), 1297–1307 (2019) Liu, Z.H.: A class of evolution hemivariational inequalities. Nonlinear Anal. TMA 36, 91–100 (1999) Liu, Z.H., Li, X.W.: Approximate controllability of fractional evolution systems with Riemann-Liouville fractional derivatives. SIAM Journal on Control and Optimization 53(4), 1920–1933 (2015) Liu, Z.H., Li, X.W.: Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations. Communications in Nonlinear Science and Numerical Simulation 18, 1362–373 (2013) Liu, Z.H., Migórski, S., Zeng, S.D.: Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces. Journal of Differential Equations 263, 3989–4006 (2017) Liu, Z.H., Motreanu, D., Zeng, S.D.: Nonlinear evolutionary systems driven by mixed variational inequalities and its applications. Nonlinear Analysis: Real World Applications 42, 409–421 (2018) Liu, Z.H., Motreanu, D., Zeng, S.D.: Generalized penalty and regularization method for differential variational-hemivariational inequalities. SIAM J. Optim. 31(2), 1158–1183 (2021) Liu, Z.H., Papageorgiou N. S.: Double phase Dirichlet problems with unilateral constraints. Journal of Differential Equations 316(15), 249–269 (2022) Liu, Z.H., Zeng, S.D., Bai, Y.R.: Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications. Fract. Calc. Appl. Anal. 19(1), 188–211 (2016). DOI: 10.1515/fca-2016-0011 Liu, Z.H., Zeng, S.D., Motreanu, D.: Partial differential hemivariational inequalities. Adv. Nonlinear Anal. 7(4), 571–586 (2018) Liu, Z.H., Zeng, S.D., Motreanu, D.: Evolutionary problems driven by variational inequalities. Journal of Differential Equations 260, 6787–6799 (2016) Migórski, S.: On existence of solutions for parabolic hemivariational inequalities. J. Comput. Applied Math. 129, 77–87 (2001) Migórski, S.: Well-posedness of constrained evolutionary differential variational-hemivariational inequalities with applications. Nonlinear Anal. Real World Appl. 67, 103593 (2022) Migórski, S., Ochal, A., Sofonea, M.: Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics 26. Springer, New York (2013) Migórski, S., Zeng, S.D.: A class of differential hemivariational inequalities in Banach spaces. J. Global Optim. 72, 761–779 (2018) Nguyen, Thi Van, Anh,: Periodic solutions to differential variational inequalities of parabolic-elliptic type. Taiwanese J. Math. 24(6), 1497–1527 (2020) Nguyen, Thi Van, Anh,: On periodic solutions to a class of delay differential variational inequalities. Evolution Equations & Control Theory 11(4), 1309–1329 (2022) Nguyen, Thi Van, Anh,: Tran, Van Thuy: On the delay differential variational inequalities of parabolic-elliptic type. Complex Variables and Elliptic Equations 67(12), 3048–3073 (2022) Nirmala, R. J., Balachandran, K., Germa, L., Trujillo, J.: Controllability of nonlinear fractional delay dynamical systems. Reports on Mathematical Physics 77(1), 87–104 (2016) Pang, J.S., Stewart, D.E.: Differential variational inequalities. Math. Program. 113, 345–424 (2008) Pang, J.S., Stewart, D.E.: Solution dependence on initial conditions in differential variational inequalities. Math. Program. 116, 429–460 (2009) Pang, X., Li, X.W., Liu, Z.H., Decay mild solutions of Hilfer fractional differential variational-hemivariational inequalities. Nonlinear Anal. Real World Appl. 71, 103834 (2023) Papageorgiou, N.S., Papalini, F., Renzacci, F.: Existence of solutions and periodic solutions for nonlinear evolution inclusions. Rend. Circolo Mat. Palermo XLVIII, 341-364 (1999) Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) Zeidler, E.: Nonlinear Functional Analysis and Applications. II A/B, Springer, New York (1990) Zeng, S.D., Liu, Z.H., Migórski, S.: A class of fractional differential hemivariational inequalities with application to contact problem. Z. Angew. Math. Phys. 69(36), pp. 23 (2018) Zhao, J., Gan, C.M., Liu, Z.H.: Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions. Acta Mathematica Sinica, English Series, Published online: September 8, 2023. https://doi.org/10.1007/s10114-023-2065-2 Zhao, J., Liu, Z.H., Vilches, E., Wen, C.F., Yao, J.C.: Optimal control of an evolution hemivariational inequality involving history-dependent operators. Commun. Nonlinear Sci. Numer. Simulat. 103, 105992 (2021)