In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity andmonotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland’s theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland’s variational principle for equilibrium problems. Via the existence of -solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.
Bianchi, M., Kassay, G., Pini, R., Existence of Equilibria via Ekeland's Principle, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 2005; 305 (2): 502-512. [doi:10.1016/j.jmaa.2004.11.042] [https://hdl.handle.net/10807/246756]
Existence of Equilibria via Ekeland's Principle
Bianchi, Monica;Pini, Rita
2005
Abstract
In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity andmonotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland’s theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland’s variational principle for equilibrium problems. Via the existence of -solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.