Article

Journal of Optimization Theory and Applications

, Volume 117, Issue 2, pp 245-266

Equilibrium Problems with Applications to Eigenvalue Problems

  • O. ChadliAffiliated withCentre des Etudes Economiques, Université Ibn Zohr
  • , N.C. WongAffiliated withDepartment of Applied Mathematics, National Sun Yat-Sen University
  • , J.C. YaoAffiliated withDepartment of Applied Mathematics, National Sun Yat-Sen University

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Abstract

In this paper, 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 Ding and Tarafdar (Ref. 1) and the generalized variational inequality studied by Cubiotti and Yao (Ref. 2). Finally, applications to a class of eigenvalue problems are given.

Equilibrium problems bifunctions (S)+ condition general nonlinear variational inequalities generalized variational inequalities eigenvalue problems