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Zbl 1141.49306
Chadli, O.; Wong, N. C.; Yao, J. C.
Equilibrium problems with applications to eigenvalue problems. (English)
[J] J. Optim. Theory Appl. 117, No. 2, 245-266 (2003). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We consider equilibrium problems and introduce the concept of $(S)_+$ condition for bifunctions. Existence results for equilibrium problems with the $(S)_+$ condition are derived. As special cases, we obtain several existence results for the generalized nonlinear variational inequality studied by [{\it X. P. Ding} and {\it E. Tarafdar}, Appl. Math. Lett. 8, No. 1, 31--36 (1995; Zbl 0824.49009)] and the generalized variational inequality studied by {\it P. Cubiotti} and {\it J.-C. Yao} [Comput. Math. Appl. 29, No. 12, 49--56 (1995; Zbl 0857.47038 )]. Finally, applications to a class of eigenvalue problems are given.

MSC 2000:: *49J40 Variational methods including variational inequalities
49J35 Minimax problems (existence)
90C47 Minimax problems

Keywords: Equilibrium problems; bifunctions; $(S)_+$ condition; general nonlinear variational inequalities; generalized variational inequalities; eigenvalue problems

Citations: Zbl 0824.49009; Zbl 0857.47038

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