Locating Cerami Sequences in a Mountain Pass Geometry
نویسنده
چکیده
Let X be a real Banach space and Φ ∈ 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 → ∞. Under our hypotheses we can find a Palais-Smale sequence for the mountain pass level with d(u n , S) → 0, but in general there is no Cerami sequence with this property and our result yields d(u n , S)/(1 + u n) → 0. Our results extend to Cerami sequences the earlier work on localization of Palais-Smale sequences due to Kuzin-Pohozaev and Ghoussoub-Preiss.
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