LOCATING CERAMI SEQUENCES IN A MOUNTAIN PASS GEOMETRY

TitleLOCATING CERAMI SEQUENCES IN A MOUNTAIN PASS GEOMETRY
Publication TypeJournal Article
Year of Publication2011
AuthorsSTUART, CA
Volume15
Issue4
Start Page569
Pagination20
Date Published2011
ISSN1083-2564
AMS46T05, 58E05
Abstract

Let X be a real Banach space and ${\Phi \in \ C^1 \ ( X, R \ )}$  a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence ${\ u_n}$ of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of ${\ u_n}$ from ${\ S}$ for certain types of set ${\ S}$ as ${\ n \to \infty}$. Under our hypotheses we can find a Palais-Smale sequence for the mountain pass level with ${\ d\ (u_n,S \ ) \to \ 0 }$ , but in general there is no Cerami sequence with this property and our result yields ${\ d\ (u_n,S \ ) / \ (1+\|u_n\| \ ) \to 0 }$. Our results extend to Cerami sequences the earlier work on localization of Palais-Smale sequences due to Kuzin-Pohozaev and Ghoussoub-Preiss.

URLhttp://www.acadsol.eu/en/articles/15/4/12.pdf
Refereed DesignationRefereed
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