Abstract
Several existence results for a class of perturbed inequality problems on various subsets of Banach spaces are proved. A concrete application to a problem from Nonsmooth Mechanics illustrates is given.
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Bocea M., Rădulescu V., Panagiotopoulos P.D. (1999) A perturbation result for a double eigenvalue hemivariational inequality with constraints and applications. J. Global Optim. 14, 137–156
Chang K.C. (1981) Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102–129
Clarke F.H. (1983) Optimization and Nonsmooth Analysis. Wiley, New-York
Dudundji J., Granas A. (1978) KKM-maps and variational inequalities.Ann. Scuola Norm. Sup. Pisa. 5, 679–682
Fichera G. (1964) Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno. Mem. Accad. Naz. Lincei 7, 91–140
Goeleven D., Motreanu D., Panagiotopoulos P.D. (1997) Semicoercive variational-hemivariational inequalities. Appl. Anal. 65, 119–134
Goeleven D., Motreanu D., Panagiotopoulos P.D. (1998) Eigenvalue problems for variational-hemivariational inequalities at resonance. Nonlinear Anal. TMA 33, 161–180
Haslinger J., Motreanu D. (2003) Hemivariational Inequalities with a general growth condition: existence and approximation. Appl. Anal. 82, 629–643
Knaster B., Kuratowski K., Mazurkiewicz S. (1929) Ein Beweis des Fixpunktsatzes für n-dimensionale simplexe. Fund. Mat. 14, 132–137
Lions J.-L., Stampacchia G. (1967) Variational inequalities. Comm. Pure Appl. Math. 20, 493–519
Motreanu D., Panagiotopoulos P.D. (1996) On the eigenvalue problem for hemivariational inequalities: existence and multiplicity of solutions. J. Math. Anal. Appl. 197, 75–89
Motreanu D., Panagiotopoulos P.D. (1997) Double eigenvalue problems for hemivariational inequalities. Arch. Rational Mech. Anal. 140, 225–252
Naniewicz Z., Panagiotopoulos P.D. (1995) Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New-York
Panagiotopoulos P.D. (1993) Hemivariational Inequalities: Application to Mechanics and Engineering. Springer-Verlag, New-York Boston Berlin
Rădulescu V., Fundo M., Panagiotopoulos P.D. (1999) Existence theorems of Hartman-Stampacchia type for hemivariational inequalities and applications. J. Global Optim. 15, 41–54
Yao J.-C. (1992) General variational inequalities in Banach spaces. Appl. Math. Lett. 5(1): 51–54
Yao J.-C. (1992) Nonlinear inequalities in Banach spaces. Comput. Math. Appl. 23(12): 95–98
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This paper is dedicated to the memory of Professor P.D. Panagiotopoulos
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Vladimirescu, C. Existence results for inequality problems on various subsets of Banach spaces and applications. J Glob Optim 37, 437–447 (2007). https://doi.org/10.1007/s10898-006-9057-5
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DOI: https://doi.org/10.1007/s10898-006-9057-5