×

Generalized quasi-variational hemi-variational inequalities. (English) Zbl 1058.49006

Summary: This paper is devoted to the existence of solutions for generalized quasi-variational hemi-variational inequalities with multivalued, discontinuous pseudomonotone operators. We obtain results which generalize and extend previously known theorems.

MSC:

49J40 Variational inequalities
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J53 Set-valued and variational analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kinderlehrer, D.; Stampacchia, G., An Introduction to Variational Inequalities and Their Applications (1980), Marcel Dekker: Marcel Dekker New York · Zbl 0457.35001
[2] Yuan, G. X.-Z, KKM Theory and Applications in Nonlinear Analysis (1999), Marcel Dekker
[3] Liu, Z. H., On quasilinear elliptic hemivariational inequalities of higher order, Acta Math. Hungar., 85, 1-2, 1-8 (1999) · Zbl 0951.35054
[4] Motreanu, D.; Panagiotopoulos, P. D., Minimax theorems and qualitative properties of the solutions of hemivariational inequalities and applications, (Nonconvex Optimization and Its Applications, Volume 29 (1999), Kluwer Academic: Kluwer Academic Dordrecht) · Zbl 0829.49005
[5] Panagiotopoulos, P. D.; Fundo, M.; Radulescu, V., Existence theorems of Hartman-Stampacchia type for hemivariational inequalities and applications, J. of Global Optimization, 15, 41-54 (1999) · Zbl 0951.49018
[6] Verma, R. U., Nonlinear variational and constrained hemivariational inequalities involving relaxed operators, Z. Angew. Math. Mech., 77, 5, 387-391 (1997) · Zbl 0886.49006
[7] Clarke, F. H., Optimization and Nonsmooth Analysis (1983), Wiley: Wiley New York · Zbl 0727.90045
[8] Mosco, U., Implicit variational problems and quasi-variational inequalities, (Nonlinear Operators and the Calculus of Variations. Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics, Volume 543 (1976), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0346.49003
[9] Browder, F. E., Nonlinear operators and nonlinear equations of evolution in Banach spaces, (Proceedings of Symposia in Pure Mathematics, Volume 18 (1976), Amer. Math. Soc: Amer. Math. Soc Providence, RI), Part 2 · Zbl 0176.45301
[10] Lunsford, M. L., Generalized variational and quasi-variational inequalities with discontinuous operators, J. of Mathematical Analysis and Applications, 214, 245-263 (1997) · Zbl 0945.49003
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.