Xiao, Yi-bin; Huang, Nan-jing Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities. (English) Zbl 1207.49012 J. Glob. Optim. 45, No. 3, 371-388 (2009). This paper deals with the Browder-Tikhonov regularization method for a class of evolution second order hemivariational inequalities with non-coercive operators. It is proved that the regularized hemivariational inequalities are solvable under certain conditions. Based on this solvability result, a sequence is constructed whose weak cluster point is a solution of an evaluation second order hemivariational inequality. Reviewer: Qamrul Hasan Ansari (Aligarh) Cited in 15 Documents MSC: 49J40 Variational inequalities 49J52 Nonsmooth analysis 40A30 Convergence and divergence of series and sequences of functions Keywords:evolution hemivariational inequalities; evolution inclusion; regularization method; convergence PDF BibTeX XML Cite \textit{Y.-b. Xiao} and \textit{N.-j. Huang}, J. Glob. Optim. 45, No. 3, 371--388 (2009; Zbl 1207.49012) Full Text: DOI References: [1] Berkovits J., Mustonen V.: Monotonicity methods for nonlinear evolution equations. Nonlinear Anal. TMA 27, 1397–1405 (1996) · Zbl 0894.34055 [2] Carl S., Heikkilä S.: Nonlinear Differential Equations in Ordered Spaces. Chapman & Hall/CRC, Boca Raton, FL (2000) · Zbl 0948.34001 [3] Carl S., Motreanu D.: Extremal solutions of quasilinear parabolic inclusions with generalized Clarke’s gradient. J. Differ. Equ. 191, 206–233 (2003) · Zbl 1042.35092 [4] Carl S., Naniewicz Z.: Vector quasi-hemivariational inequalities and discontinuous elliptic systems. J. Global Optim. 34, 609–634 (2006) · Zbl 1090.49005 [5] Carl S., Le V.K., Motreanu D.: Existence and comparison results for quasilinear evolution hemivariational inequalities. Electron. J. Differ. Equ. 57, 1–17 (2004) · Zbl 1053.49005 [6] Carl S., Le V.K., Motreanu D.: The sub-supersolutio method and extremal solutions for quasilinear hemivariational inequalities. Differ. Integral Equ. 17, 165–178 (2004) · Zbl 1164.35301 [7] Carl S., Le V.K., Motreanu D.: Nonsmooth Variational Problems and their Inequalities, Comparison Principles and Applications. Springer-Verlag, Berlin (2005) · Zbl 1109.35004 [8] Clarke F.H.: Optimization and Nonsmooth Analysis. SIAM, Philadelphia (1990) · Zbl 0696.49002 [9] Denkowski Z., Migorski S.: Existence of solutions to evolution second order hemivariational inequalities with multivalued damping. Syst. Model. Optim. 166, 203–215 (2005) · Zbl 1082.74036 [10] Denkowski Z., Migorski S., Papageorgiou N.S.: An Introduction to Nonlinear Analysis: Applications. Kluwer Academic Publishers, Boston, Dordrecht, London (2003) [11] Giannessi F., Khan A.A.: Regularization of non-coercive quasi variational inequalities. Control Cybern. 29, 91–110 (2000) · Zbl 1006.49004 [12] Liu Z.H.: Some convergence results for evolution hemivariational inequalities. J. Global Optim. 29, 85–95 (2004) · Zbl 1061.49011 [13] Liu Z.H.: Browder-Tikhonov regularization on non-coercive evolution hemivariational inequalities. Inverse Probl. 21, 13–20 (2005) · Zbl 1078.49006 [14] Migorski S.: Boundary hemivariational inequalities of hyperbolic type and applications. J. Global Optim. 31, 505–533 (2005) · Zbl 1089.49014 [15] Motreanu D., Panagiotopoulos P.D.: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities and Applications, Nonconvex Optimization and Its Applications, vol. 29. Kluwer Academic, Dordrecht (1999) · Zbl 1060.49500 [16] Naniewicz Z., Panagiotopoulos P.D.: Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York (1995) · Zbl 0968.49008 [17] Ochal A.: Existence results for evolution hemivariational inequalities of second order. Nonlinear Anal. TMA 60, 1369–1391 (2005) · Zbl 1082.34052 [18] Panagiotopoulos P.D.: Coercive and semicoercive hemivariational inequalities. Nonlinear Anal. TMA 16, 209–231 (1991) · Zbl 0733.49012 [19] Panagiotopoulos P.D.: Hemivariational Inequalities, Applications in Mechanics and Engineering. Springer-Verlag, Berlin (1993) · Zbl 0826.73002 [20] Panagiotopoulos P.D.: Hemivariational inequalitiy and fan-variational inequality. New applications and results. Atti. Sem. Mat. Fis. Univ. Modena XLIII, 159–191 (1995) · Zbl 0843.49006 [21] Xiao Y.B., Huang N.J.: Sub-supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities. Nonlinear Anal. TMA 66, 1739–1752 (2007) · Zbl 1110.49012 [22] Xiao Y.B., Huang N.J.: Generalized quasi-variational-like hemivariational inequalities. Nonlinear Anal. TMA 69, 637–646 (2008) · Zbl 1143.49009 [23] Zeidler E.: Nonlinear Functional Analysis and its Applications, vol. II. Springer-verlag, Berlin (1990) · Zbl 0684.47029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.