The Mountain-Pass Theorem

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On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014, background): “Arcoya and Carmona extended in [8, Theorem 3.4] the results of Pucci and Serrin to a wide class of continuous func- tionals not necessarily differentiable.”
Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent (2008, background): “By Lemmas 1 and 2 and the mountain pass theorem of Ambrosetti and Rabinowitz [4] (see also Pucci and Serrin [29] for the case of mountains of zero altitude), we deduce the existence of a sequence (un) ⊂ E such that Jλ(un) → c > 0 and J ′λ(un) → 0 (in E ) as n → ∞.”
On the structure of the critical set of non-differentiable functions with a weak compactness condition (2010, background): “4 comes out from the famous Pucci and Serrin's multiple critical point result 8 , Corollary 1], while Theorem 3.”
N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, methodology): “Let {un} be a Cerami sequence in W1,N0 (Ω) such that (1 + ‖un‖) ‖DJ(un)‖ → 0 J(un) → c i.e. (1 + ‖un‖) ∣∣∣∣∣ ∫ Ω |∇un|N−2 ∇un∇vdx − ∫ Ω f (x, un)vdx ∣∣∣∣∣ ≤ εn ‖v‖ (4.16) 1 N ‖un‖N − ∫ Ω F(x, un)dx → c where εn n→∞→ 0.”