A Version of Zhong’s Coercivity Result for a General Class of Nonsmooth Functionals

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.