On the relation between the weak Palais-Smale condition and coercivity given by Zhong

摘要

In this paper, we discuss Zhong's result that the weak Palais-Smale condition implies coercivity under some assumption given in [C.-K. Zhong, A generalization of Ekeland's variational principle and application to the study of the relation between the weak P.S. condition and coercivity, Nonlinear Anal. 29 (1997) 1421-1431]. We also give a simple proof of Zhong's result. Further we generalize the result of Caklovic, Li and Willem [L. Caklovic, S.J. Li, M. Willem, A note oil Palais-Smale condition and coercivity, Differential Integral Equations 3 (1990) 799-800]. (c) 2008 Elsevier Ltd. All rights reserved.