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By Vítor Neves


Critical points of uniformly differentiable functional Let E be a real Banach space and f: E → R a smooth (C 1-Frechét) functional. Suppose f verifies the Palais-Smale condition (PS) Any sequence xn ∈ E N such that f(xn) is bounded and that f ′ (xn) → 0, has a convergent subsequence. and the mountain pass geometry for (e, r) ∈ E×]0, +∞[ (MPG) r < ‖e‖ max{f(0), f(e)} < inf{f(x) | x ∈ E ∧ ‖x ‖ = r} ∈ R

Year: 2013
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