Abstract
If we consider, the solvability of complementarity problems in infinite-dimensional case, we observe that the compactness or the complete continuity of operators used in the definition of many complementarity problems must be imposed as assumption.
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References
ALTMAN, M. 1. A fixed point theorem in Hilbert spaces. Bull. Acad. Polon. Sci. cl. Iii 5 (1957), 19–22.
BERGE, C. 1. Topological Spaces. Oliver and Boyd, Edinburgh (1963).
BREZIS, H., NIRENBERG, L. and STAMPACCHIA, G. 1. A remark on Ky Fan’s minimax principle. Boll. Un. Mat. Ital. 6 (1972), 293–300.
BROWDER, F. E. 1. Existence theorems for nonlinear partial differential equations. Proc. Sympos. Pure Math. 16 Amer. Math. Soc., Providence R. I. (1970), 1–60.
BROWDER, F. E. 2. Nonlinear eigenvalue problems and (Galerkin approximations. Bull. Amer. Math. Soc. 74 (1968), 651–656.
BROWDER, F. E. 3. Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms. Proc. Sympos. Pure Math. 23 Amer. Math. Soc. Providence R. I. (1973) 269–286.
BROWDER, F. E. 4. Fixed point theory and nonlinear problems. Bull. Amer. Math. Soc. 9 (1983), 1–39.
CIORXÇŽNESCU, I. 1. Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems. Kluwer Academic Publishers, Dordrecht, Boston, London (1990).
CUBIOTI, P. l. General nonlinear variational inequalities with (S) 1+ operators. Preprint, University of Messina (1996).
CUBIOTI, P. and YAO, J. C. 1. Multivalued (S) +1 operators and generalized variational inequalities. Computers Math. Applic. 29 Nr. 12 (1995), 49–56.
DIESTEL, J. 1. Geometry of Banach Spaces. Selected Topics. Lecture Notes in Math. Springer-Verlag Nr. 485. Guo. J. S. and Yao, J. C.
DIESTEL, J. 1. Variational inequalities with nonmonotone operators. J. Opt. Theory Appl. 80 Nr. 4 (1994).
ISAC, G. 1. Nonlinear complementarity problem and Galerkin method. J. Math. Anal. Appl. 108 (1985), 563–574.
ISAC, G. 2. Complementarity Problems. Lecture Notes in Mathematics, Nr. 1528, Springer-Verlag, (1992).
ISAC, G. 3. Problèmes de Complémentarité (En dimension infinie)(minicours). Publ. Dép. Math. Univ. Limoges, (France) (1985).
ISAC, G. 4. On an Altman type fixed point theorem on convex cones. Rocky Mountain J. Math., 25 Nr. 2 (1995).
ISAC, G. 5. On some generalization of Karamardian’s Theorem on the complementarity problem. Bolletino U. M. I. (7), 2-B (1988), 323–332.
ISAC, G. and GOWDA, M. S. 1. Operators of class (S) 1+ , Altman’s condition and the complementarity problem. J. Fac. Science, The Univ. of Tokyo, Sec. Ia, Vol. 40, Nr. 1 (1993), 1–16.
ISAC, G. and THERA, M. 1. Complementarity problem and the existence of the postcritical equilibrium state of a thin elastic plate. J. Opt. Theory Appl. 58 (1988), 241–257.
ISAC, G. and Thera, M. 2. A variational principle. Application to the nonlinear complementarity problem. In. Nonlinear and Convex Analysis (Eds. B. L. Lin and S. Simons), Marcel Dekker Inc., New York (1987).
LAN K. and WEBB, J. 1. Variational inequalities and fixed point theorems for Pm-maps. J. Math. Anal. Appl. 224 (1998), 102–116.
LIONS, J. L. 1. Quelques Méthods de Résolutoin des Problèmes aux Limites Non-linéaires. Dunod, GauthiersVillars, Paris (1969).
LIPKIN, L. J. 1. Weak continuity and compactness of nonlinear mappings. Nonlinear Anal., Theory Meth. Appl. 5 (1981), 1257–1263.
MARINESCU, GH. 1. Espaces Vectoriels Pseudo-topologiques et Théorie des distributions. Veb. Deutscher Verlag Des Wissenschaften, Berlin (1965).
SCHAEFER, H. H. 1. Topological Vector Spaces. The Mc.Millan Company (1966).
SHINBROT, M. 1. A fixed point theorem and some applications. Arch. Rational Mech. Anal. 17 (1965), 255–271.
THÉRA, M. 1. Existence results for the nonlinear complementarity problem and applications to nonlinear analysis. J. Math. Anal. Appl. 154 (1991), 572–584.
VAINBERG, M. M. 1. Variational Methods for the study of nonlinear operators. Holden-Day Inc. San-Francisco, London (1964).
ZHOU, Y. and HUANG, Y. 1. Several existence theorems for the nonlinear complementarity problem. J. Math. Anal. Appl. 202 (1996), 776–784.
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Isac, G. (2000). Conditions (S)+ and (S) 1+ : Applications to Complementarity Theory. In: Topological Methods in Complementarity Theory. Nonconvex Optimization and Its Applications, vol 41. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3141-5_9
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DOI: https://doi.org/10.1007/978-1-4757-3141-5_9
Publisher Name: Springer, Boston, MA
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