A note on Palais-Smale condition in the sense of Szulkin
It has been observed [\textit{L. Caklovic}, \textit{Sh. Li} and \textit{M. Willem}, Differ. Integral Equ. 3, No. 4, 799-800 (1990; see the review above)] that, for a Gâteaux differentiable lower semicontinuous function bounded from below on a Banach space, the Palais-Smale condition implies coercivity. Recently, critical point theory has been generalized by \textit{A. Szulkin} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 3, 77-109 (1986; Zbl 0612.58011)] to the nonsmooth case, and for this, he introduced a compactness condition of Palais-Smale type. Our aim is to generalize Caklovic-Li-Willem's result [loc. cit.] to the nonsmooth case using the Palais-Smale condition as given by Szulkin.
scientific article; zbMATH DE number 459189