Acta mathematica scientia, Series B >
DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES
Received date: 2015-12-31
Revised date: 2016-04-29
Online published: 2017-02-25
Supported by
Project supported by NNSF of China (11671101), the National Science Center of Poland Under Maestro Advanced Project (UMO-2012/06/A/ST1/00262), and Special Funds of Guangxi Distinguished Experts Construction Engineering.
In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem.
Zhenhai LIU , Shengda ZENG . DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES[J]. Acta mathematica scientia, Series B, 2017 , 37(1) : 26 -32 . DOI: 10.1016/S0252-9602(16)30112-6
[1] Browder F E. Nonlinear monotone operators and convex sets in Banach spaces. Bull Amer Math Soc, 1965, 71:780-785
[2] Chen X J,Wang Z Y. Differential variational inequality approach to dynamic games with shared constraints. Math Program, 2014, 146:379-408
[3] Gwinner J. On the p-version approximation in the boundary element method for a variational inequality of the second kind modelling unilateral contact and given friction. Appl Numer Math, 2009, 59:2774-2784
[4] Gwinner J. hp-FEM convergence for unilateral contact problems with Tresca friction in plane linear elastostatics. J Comput Appl Math, 2013, 254:175-184
[5] Han L, Pang J S. Non-Zenoness of a class of differential quasi-variational inequalities. Math Program, 2010, 121:171-199
[6] Ke T D, Loi N V, Obukhovskii V. Decay solutions for a class of fractional differential variational inequalities. Fract Calc Appl Anal, 2015, 18:531-553
[7] Kamemsloo M, Obukhovskii V, Zecca P. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space. Berlin:Water de Gruyter, 2001
[8] Li X J, Yong J M. Optimal Control Theory for infinite Dimensional Systems. Boster:Birkhäuser, 1995
[9] Liu Z H, Zeng S D, Motreanu D. Evolutionary problems driven by variational inequalities. J Differ Equ, 2016, 260:6787-6799
[10] Liu Z H, Loi N V, Obukhovskii V. Existence and global bifurcation of periodic solutions to a class of differential variational inequalities. Int J Bifurcation Chaos, 2013, 23(7):ID:1350125
[11] Loi N V. On two-parameter global bifurcation of periodic solutions to a class of differential variational inequalities. Nonlinear Anal, 2015, 122:83-99
[12] Migórski S, Ochal A, Sofonea M. Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics 26. New York:Springer, 2013
[13] Papageorgiou N S, Kyritsi-Yiallourou S T. Handbook of Applied Analysis. New York:Springer, 2009
[14] Pang J S, Stewart D E. Differential variational inequalities. Math Program, 2008, 113:345-424
[15] Pang J S, Stewart D E. Solution dependence on initial conditions in differential variational variational inequalities. Math Program, 2009, 116:429-460
[16] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York:Springer-Verlag, 1983
[17] Rykaczewski K. Approximate controllability of differential inclusions in Hilbert spaces. Nonlinear Anal, 2012, 75:2701-2712
[18] Wang X, Huang N J. A class of differential vector variational inequalities in finite dimensional spaces. J Optim Theory Appl, 2014, 162:633-648
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