Critical point theory and its applications

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Existence and multiplicity of solutions for a class of fourth-order elliptic equations in R^N (2012, unknown): “4 in [13], we can prove the embedding E1 ↩→ Ls(RN) is compact for any s ∈ [2, 2∗), where E1 =  u ∈ H :  RN (|∆u| 2 + |∇u|2 + V (x)u2)dx < ∞  .”
Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations (2007, background): “From a theorem in [4],this complete the proof.”
Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, methodology): “We have the following versions of the Mountain Pass Theorem (see [5, 10, 12, 13]): Lemma 1 Let (X,‖ · ‖X) be a real Banach space and let I ∈ C1(X,R) satisfy the (C)c condition for any c ∈ R, I (0) = 0 and (i) There are constants ρ,α > 0 such that I |∂Bρ ≥ α.”
Multiplicity of high energy solutions for superlinear Kirchhoff equations (2012, background): “4), there is a large quantity of study on the existence and multiplicity of solutions in the literature, we refer to [20–25] and the references therein.”