Abstract and Applied Analysis

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

D. Motreanu, V. V. Motreanu, and D. Paşca

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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.

Article information

Abstr. Appl. Anal., Volume 7, Number 11 (2002), 601-612.

Received: 27 October 2001
First available in Project Euclid: 14 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E30: Variational principles 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 49K27: Problems in abstract spaces [See also 90C48, 93C25]


Motreanu, D.; Motreanu, V. V.; Paşca, D. A version of Zhong′s coercivity result for a general class of nonsmooth functionals. Abstr. Appl. Anal. 7 (2002), no. 11, 601--612. doi:10.1155/S1085337502207058. https://projecteuclid.org/euclid.aaa/1050348308

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