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Equilibrium problems with applications to eigenvalue problems. (English) Zbl 1141.49306
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:
 49J40 Variational methods including variational inequalities 49J35 Minimax problems (existence) 90C47 Minimax problems
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