Abstract
We give some versions of theorems of Hartman-Stampacchia's type for the case of Hemivariational Inequalities on compact or on closed and convex subsets in infinite and finite dimensional Banach spaces. Several problems from Nonsmooth Mechanics are solved with these abstract results.
Similar content being viewed by others
References
Clarke, F. (1983) Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983.
Holmes, R.B. (1975) Geometric Functional Analysis and its Applications, Springer-Verlag, New York.
Hartman, G.J. & Stampacchia, G. (1966) On some nonlinear elliptic differential equations, Acta Math. 115, 271–310.
Kavian, O. (1993) Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Springer-Verlag, Paris, Berlin, Heidelberg, New York, London, Tokyo, Hong Kong, Barcelona, Budapest, 1993.
Kinderlehrer, D. & Stampacchia, G. (1980) An Introduction to Variational Inequalities, Academic Press, New York.
Naniewicz, Z. & Panagiotopoulos, P.D. (1995) Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker, New York.
Oettli, W. & Prager, W. (1966) Flow in networks with amplification and coupling, Unternehmensforschung 10, 42–58.
Panagiotopoulos, P.D. (1985) Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functionals, Birkháuser-Verlag, Boston, Basel (Russian translation MIR Publ., Moscow, 1989).
Panagiotopoulos, P.D. (1993) Hemivariational Inequalities: Applications to Mechanics and Engineering, Springer-Verlag, New York, Boston, Berlin.
Pascali, D. & Sburlan, S. (1978) Nonlinear Mappings of Monotone Type, Sijthoff and Noordhoff, The Netherlands.
Prager, W. (1965) Problems of Network Flow, Z.A.M.P. 16, 185–193.
Schaefer, H. H. (1966) Topological Vector Spaces, Macmillan Series in Advances Mathematics and Theoretical Physics, New York.
Thera, M. (1987) A note on the Hartman-Stampacchia theorem, in: Lakshmikantham, (ed.) Proceedings of the International Conference on Nonlinear Analysis and Applications M. Dekker, Arlington, TX, 573–577.
Yao J.C. (1992) Variational Inequality, Appl. Math. Lett. 5, 39–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Panagiotopoulos, P.D., Fundo, M. & Rădulescu, V. Existence Theorems of Hartman–Stampacchia Type for Hemivariational Inequalities and Applications. Journal of Global Optimization 15, 41–54 (1999). https://doi.org/10.1023/A:1008340210469
Issue Date:
DOI: https://doi.org/10.1023/A:1008340210469