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On a class of variational-hemivariational inequalities involving upper semicontinuous set-valued mappings. (English) Zbl 1474.49026

Summary: This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results.

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
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[1] Costea, N.; Lupu, C., On a class of variational-hemivariational inequalities involving set valued mappings, Advances in Pure and Applied Mathematics, 1, 2, 233-246 (2010) · Zbl 1215.47054
[2] Tang, G.-J.; Huang, N.-J., Existence theorems of the variational-hemivariational inequalities, Journal of Global Optimization, 56, 2, 605-622 (2013) · Zbl 1272.49019
[3] Motreanu, D.; Rǎdulescu, V., Existence results for inequality problems with lack of convexity, Numerical Functional Analysis and Optimization, 21, 7-8, 869-884 (2000) · Zbl 0981.49009
[4] Zhang, Y.; He, Y., On stably quasimonotone hemivariational inequalities, Nonlinear Analysis: Theory, Methods & Applications, 74, 10, 3324-3332 (2011) · Zbl 1245.49018
[5] Zhang, Y. L.; He, Y. R., The hemivariational inequalities for an upper semicontinuous set-valued mapping, Journal of Optimization Theory and Applications, 156, 3, 716-725 (2013) · Zbl 1301.49029
[6] Panagiotopoulos, P. D.; Fundo, M.; Rǎdulescu, V., Existence theorems of Hartman-Stampacchia type for hemivariational inequalities and applications, Journal of Global Optimization, 15, 1, 41-54 (1999) · Zbl 0951.49018
[7] Costea, N.; Rǎdulescu, V., Hartman-stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities, Applicable Analysis, 89, 2, 175-188 (2010) · Zbl 1184.49022
[8] Tang, G.-J.; Huang, N.-J., Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities, Applied Mathematics and Mechanics, 32, 10, 1345-1356 (2011) · Zbl 1258.47078
[9] Tang, G.-J.; Huang, N.-J., Strong convergence of an inexact projected subgradient method for mixed variational inequalities, Optimization, 63, 4, 601-615 (2014) · Zbl 1291.49012
[10] Wang, Z. B.; Huang, N. J., Degree theory for a generalized set-valued variational inequality with an application in Banach spaces, Journal of Global Optimization, 49, 2, 343-357 (2011) · Zbl 1210.49016
[11] Xia, F.-Q.; Huang, N.-J., An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities, Computers and Mathematics with Applications, 62, 12, 4596-4604 (2011) · Zbl 1236.49023
[12] Zhong, R.-Y.; Huang, N.-J., Stability analysis for minty mixed variational inequality in reflexive Banach spaces, Journal of Optimization Theory and Applications, 147, 3, 454-472 (2010) · Zbl 1218.49032
[13] Panagiotopoulos, P. D., Nonconvex energy functions. Hemivariational inequalities and substationarity principles, Acta Mechanica, 48, 3-4, 111-130 (1983) · Zbl 0538.73018
[14] Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions (1985), Basel, Switzerland: Birkhäuser, Basel, Switzerland · Zbl 0579.73014
[15] Panagiotopoulos, P. D., Coercive and semicoercive hemivariational inequalities, Nonlinear Analysis, 16, 3, 209-231 (1991) · Zbl 0733.49012
[16] Panagiotopoulos, P. D., Hemivariational Inequalities: Applications in Mechnics and Engineering (1993), Berlin, Germany: Springer, Berlin, Germany · Zbl 0826.73002
[17] Clarke, F. H., Optimization and Nonsmooth Analysis (1983), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0582.49001
[18] Naniewicz, Z.; Panagiotopoulos, P. D., Mathematical Theory of Hemivariational Inequalities and Applications (1995), New York, NY, USA: Marcel Dekker, New York, NY, USA · Zbl 0968.49008
[19] Carl, S., Existence of extremal solutions of boundary hemivariational inequalities, Journal of Differential Equations, 171, 2, 370-396 (2001) · Zbl 1180.35255
[20] Carl, S.; Le, V. K.; Motreanu, D., Existence and comparison principles for general quasilinear variational-hemivariational inequalities, Journal of Mathematical Analysis and Applications, 302, 1, 65-83 (2005) · Zbl 1061.49007
[21] Carl, S.; Le, V. K.; Motreanu, D., Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications (2007), New York, NY, USA: Springer, New York, NY, USA · Zbl 1109.35004
[22] Xiao, Y.-B.; Huang, N.-J., Sub-super-solution method for a class of higher order evolution hemivariational inequalities, Nonlinear Analysis: Theory, Methods & Applications, 71, 1-2, 558-570 (2009) · Zbl 1162.49015
[23] Migórski, S.; Ochal, A., Boundary hemivariational inequality of parabolic type, Nonlinear Analysis: Theory, Methods & Applications, 57, 4, 579-596 (2004) · Zbl 1050.35043
[24] Park, J. Y.; Ha, T. G., Existence of antiperiodic solutions for hemivariational inequalities, Nonlinear Analysis: Theory, Methods & Applications, 68, 4, 747-767 (2008) · Zbl 1151.47056
[25] Park, J. Y.; Ha, T. G., Existence of anti-periodic solutions for quasilinear parabolic hemivariational inequalities, Nonlinear Analysis: Theory, Methods & Applications, 71, 7-8, 3203-3217 (2009) · Zbl 1178.35227
[26] Goeleven, D.; Motreanu, D.; Panagiotopoulos, P. D., Eigenvalue problems for variational-hemivariational inequalities at resonance, Nonlinear Analysis: Theory, Methods & Applications, 33, 2, 161-180 (1998) · Zbl 0939.74021
[27] Liu, Z., Existence results for quasilinear parabolic hemivariational inequalities, Journal of Differential Equations, 244, 6, 1395-1409 (2008) · Zbl 1139.35006
[28] Costea, N., Existence and uniqueness results for a class of quasi-hemivariational inequalities, Journal of Mathematical Analysis and Applications, 373, 1, 305-315 (2011) · Zbl 1201.49009
[29] Peng, Z.; Liu, Z., Evolution hemivariational inequality problems with doubly nonlinear operators, Journal of Global Optimization, 51, 3, 413-427 (2011) · Zbl 1254.90258
[30] Xiao, Y.-B.; Huang, N.-J., Well-posedness for a class of variational-hemivariational inequalities with perturbations, Journal of Optimization Theory and Applications, 151, 1, 33-51 (2011) · Zbl 1228.49026
[31] Bianchi, M.; Pini, R., Coercivity conditions for equilibrium problems, Journal of Optimization Theory and Applications, 124, 1, 79-92 (2005) · Zbl 1064.49004
[32] Daniilidis, A.; Hadjisavvas, N., Coercivity conditions and variational inequalities, Mathematical Programming B, 86, 2, 433-438 (1999) · Zbl 0937.49003
[33] Facchinei, F.; Pang, J.-S., Finite-Dimensional Variational Inequalities and Complementarity Problems, I (2003), New York, NY, USA: Springer, New York, NY, USA · Zbl 1062.90001
[34] Konnov, I. V.; Dyabilkin, D. A., Nonmonotone equilibrium problems: coercivity conditions and weak regularization, Journal of Global Optimization, 49, 4, 575-587 (2011) · Zbl 1242.90262
[35] Deimling, K., Nonlinear Functional Analysis (1985), Berlin, Germany: Springer, Berlin, Germany · Zbl 0559.47040
[36] Qiao, F.; He, Y., Strict feasibility of pseudomonotone set-valued variational inequalities, Optimization, 60, 3, 303-310 (2011) · Zbl 1237.90236
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