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A Generalized Palais-Smale Condition in the Fréchet space setting

Published 21 Oct 2014 in math.DG | (1410.5638v4)

Abstract: We extend the Palais-Smale condition to Keller's $C_c1$-functionals on Fr\'{e}chet spaces. Using this condition together with Ekeland's variational principle, we obtain some results regarding the existence of minima. In this setting, we prove that the Palais-Smale condition for functionals bounded below implies the coercivity.

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