zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Pseudo-monotone complementarity problems in Hilbert space. (English) Zbl 0795.90071
Summary: Some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.

90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C48Programming in abstract spaces
49J40Variational methods including variational inequalities
[1]Karamardian, S.,Generalized Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 8, pp. 161-168, 1971. · Zbl 0208.46301 · doi:10.1007/BF00932464
[2]Allen, G.,Variational Inequalities, Complementarity Problems, and Duality Theorems, Journal of Mathematical Analysis and Applications, Vol. 58, pp. 1-10, 1977. · Zbl 0383.49005 · doi:10.1016/0022-247X(77)90222-0
[3]Bazaraa, M. S., Goode, J. J., andNashed, M. Z.,A Nonlinear Complementarity Problem in Mathematical Programming in Banach Space, Proceedings of the American Mathematical Society, Vol. 35, pp. 165-170, 1972. · doi:10.1090/S0002-9939-1972-0300163-5
[4]Borwein, J. M.,Alternative Theorems for General Complementarity Problems, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York, New York, Vol. 259, pp. 194-203, 1985.
[5]Dash, A. T., andNanda, S.,A Complementarity Problem in Mathematical Programming in Banach Space, Journal of Mathematical Analysis and Applications, Vol. 98, pp. 328-331, 1984. · Zbl 0547.90099 · doi:10.1016/0022-247X(84)90251-8
[6]Gowda, M. S., andSeidman, T. I.,Generalized Linear Complementarity Problems, Mathematical Programming, Vol. 46, pp. 329-340, 1990. · Zbl 0708.90089 · doi:10.1007/BF01585749
[7]Habetler, G. J., andPrice, A. L.,Existence Theory for Generalized Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 7, pp. 223-239, 1971. · Zbl 0212.24001 · doi:10.1007/BF00928705
[8]Harker, P. T., andPang, J. S.,Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990. · Zbl 0734.90098 · doi:10.1007/BF01582255
[9]Isac, G.,On Some Generalization of Karamardian’s Theorem on the Complementarity Problem, Bollettino UMI, Vol. 7, 2-B, pp. 323-332, 1988.
[10]Isac, G.,Nonlinear Complementarity Problem and Galerkin Method, Journal of Mathematical Analysis and Applications, Vol. 108, pp. 563-574, 1985. · doi:10.1016/0022-247X(85)90045-9
[11]Isac, G.,Problèmes de Complémentarité [en Dimension Infinie], Minicourse, Publication du Département de Mathématique, Université de Limoges, Limoges, France, 1985.
[12]Isac, G., andThéra M.,Complementarity Problem and the Existence of the Post-Critical Equilibrium State of a Thin Elastic Plate, Journal of Optimization Theory and Applications, Vol. 58, pp. 241-257, 1988. · Zbl 0631.49005 · doi:10.1007/BF00939684
[13]Karamardian, S.,Complementarity Problems over Cones with Monotone and Pseudo-Monotone Maps, Journal of Optimization Theory and Applications, Vol. 18, pp. 445-454, 1976. · Zbl 0304.49026 · doi:10.1007/BF00932654
[14]Moré, J. J.,Coercivity Conditions in Nonlinear Complementarity Problems, SIAM Review, Vol. 16, pp. 1-16, 1974. · Zbl 0272.65041 · doi:10.1137/1016001
[15]Nanda, S., andNanda, S.,A Nonlinear Complementarity Problem in Mathematical Programming in Hilbert Space, Bulletin of the Australian Mathematical Society, Vol. 20, pp. 233-236, 1979. · Zbl 0404.90091 · doi:10.1017/S000497270001090X
[16]Barbu, V., andPrecupanu, T.,Convexity and Optimization in Banach Spaces, Sijthoff and Noordhoff, Bucharest, Romania, 1978.
[17]Hartman, G. J., andStampacchia, G.,On Some Nonlinear Elliptic Differential Functional Equations, Acta Mathematica, Vol. 115, pp. 271-310, 1966. · Zbl 0142.38102 · doi:10.1007/BF02392210
[18]Kinderlehrer, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980.
[19]Théra, M.,A Note on the Hartman-Stampacchia Theorem, Nonlinear Analysis and Applications, Edited by V. Lakshmikantham, Marcel Dekker, New York, New York, pp. 573-577, 1987.
[20]Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, New York, New York, 1975.
[21]Karamardian, S., andSchaible, S.,Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, Vol. 66, pp. 37-46, 1990. · Zbl 0679.90055 · doi:10.1007/BF00940531
[22]Karamardian, S., andSchaible, S.,First-Order Characterizations of Generalized Monotone Maps, Manuscript, Graduate School of Management, University of California, Riverside, California, 1989.
[23]Bourbaki, N.,Topological Vector Spaces, Chapters 1-5, Translated by H. G. Eggleston and S. Madan, Springer-Verlag, Berlin, Germany, 1987.
[24]Fan, K.,A Generalization of the Alaoglu-Bourbaki Theorem and Its Applications, Mathematische Zeitschrift, Vol. 88, pp. 48-60, 1965. · Zbl 0135.34402 · doi:10.1007/BF01112692
[25]Do, C.,Bifurcation Theory for Elastic Plates Subjected to Unilateral Conditions, Journal of Mathematical Analysis and Applications, Vol. 60, pp. 435-448, 1977. · Zbl 0364.73030 · doi:10.1016/0022-247X(77)90033-6