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

Abstract

A version of Zhong′s coercivity result (1997) is established for nonsmooth functionals expressed as a sum $\Phi +\Psi$, where $\Phi$ is locally Lipschitz and $\Psi$ 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.