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 [X. P. Ding and E. Tarafdar, Appl. Math. Lett. 8, No. 1, 31–36 (1995; Zbl 0824.49009)] and the generalized variational inequality studied by P. Cubiotti and 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.


49J40 Variational inequalities
49J35 Existence of solutions for minimax problems
90C47 Minimax problems in mathematical programming
Full Text: DOI


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