On the relation between the weak Palais–Smale condition and coercivity given by Zhong |
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Authors: | Tomonari Suzuki |
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Institution: | Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan |
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Abstract: | 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 on Palais–Smale condition and coercivity, Differential Integral Equations 3 (1990) 799–800]. |
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Keywords: | 49K27 |
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