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

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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. Copyright © 2002 Hindawi Publishing Corporation.

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Motreanu, D., Motreanu, V. V., & Paçca, D. (2002). A version of Zhong’s coercivity result for a general class of nonsmooth functionals. Abstract and Applied Analysis, 7(11), 601–612. https://doi.org/10.1155/S1085337502207058

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