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

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 function...

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Main Authors: D. Motreanu, V. V. Motreanu, D. Paşca
Format: Article
Language:English
Published: Hindawi Limited 2002-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/S1085337502207058
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spelling doaj-0f0f0d9dc97e4740a248cda4d92135ea2020-11-24T22:09:13ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092002-01-0171160161210.1155/S1085337502207058A version of Zhong's coercivity result for a general class of nonsmooth functionalsD. Motreanu0V. V. Motreanu1D. Paşca2Département de Mathématiques, Université de Perpignan, Perpignan 66860, FranceDépartement de Mathématiques, Université de Perpignan, Perpignan 66860, FranceMathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USAA 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.http://dx.doi.org/10.1155/S1085337502207058
collection DOAJ
language English
format Article
sources DOAJ
author D. Motreanu
V. V. Motreanu
D. Paşca
spellingShingle D. Motreanu
V. V. Motreanu
D. Paşca
A version of Zhong's coercivity result for a general class of nonsmooth functionals
Abstract and Applied Analysis
author_facet D. Motreanu
V. V. Motreanu
D. Paşca
author_sort D. Motreanu
title A version of Zhong's coercivity result for a general class of nonsmooth functionals
title_short A version of Zhong's coercivity result for a general class of nonsmooth functionals
title_full A version of Zhong's coercivity result for a general class of nonsmooth functionals
title_fullStr A version of Zhong's coercivity result for a general class of nonsmooth functionals
title_full_unstemmed A version of Zhong's coercivity result for a general class of nonsmooth functionals
title_sort version of zhong's coercivity result for a general class of nonsmooth functionals
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2002-01-01
description 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.
url http://dx.doi.org/10.1155/S1085337502207058
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