A Critical Point Theory for Equilibrium Problems
Professor Ouayl Chadli
Department of Economics, Ibn Zohr University,
Faculty of Economics and Social Sciences, Morocco
ABSTRACT: The theory of Equilibrium Problems (EP) has emerged as an interesting branch of applicable
mathematics. This theory provides a general and convenient format to write and investigate many
problems and becomes a rich source of inspiration and motivation for the study of a large number of
problems arising in economics, optimization, and operation research in a general and unified way.
There are a substantial number of papers on existence results for solving equilibrium problems based
on different relaxed monotonicity notions and various compactness assumptions. Inspired by
some results from critical point theory, we propose to study equilibrium problems by means
of a general Palais-Smale condition adapted to bifunctions. We introduce the notion of critical points
for equilibrium problems and we give some existence results for (EP) with lack of compacity. Some
other applications have been also considered.
Key words: Critical point; Equilibrium Problems; Palais-Smale condition; Ekeland's principle.
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