Abstract and Applied Analysis
Volume 7 (2002), Issue 11, Pages 601-612

A version of Zhong's coercivity result for a general class of nonsmooth functionals

D. Motreanu,1 V. V. Motreanu,1 and D. Paşca2

1Département de Mathématiques, Université de Perpignan, Perpignan 66860, France
2Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester 01609-2280, MA, USA

Received 27 October 2001

Copyright © 2002 D. Motreanu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A version of Zhong's coercivity result (1997) is established for nonsmooth functionals expressed as a sum Φ+Ψ, where Φ is locally Lipschitz and Ψ is convex, lower semicontinuous, and proper. This is obtained as a consequence of a general result describing the asymptotic behavior of the functions verifying the above structure hypothesis. Our approach relies on a version of Ekeland's variational principle. In proving our coercivity result we make use of a new general Palais-Smale condition. The relationship with other results is discussed.