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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502207058 |
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| _version_ | 1832565489592696832 |
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| author | D. Motreanu V. V. Motreanu D. Paşca |
| author_facet | D. Motreanu V. V. Motreanu D. Paşca |
| author_sort | D. Motreanu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0f0f0d9dc97e4740a248cda4d92135ea |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0f0f0d9dc97e4740a248cda4d92135ea2025-02-03T01:07:28ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/S1085337502207058 |
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