Abstract and Applied Analysis
Volume 7 (2002), Issue 11, Pages 601-612
doi:10.1155/S1085337502207058
A version of Zhong's coercivity result for a general class of nonsmooth functionals
D. Motreanu1
, V.V. Motreanu1
and D. Paşca3
1Département de Mathématiques, Université de Perpignan, Perpignan 66860, France
3Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester 01609-2280, MA, USA
Abstract
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.