The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations

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The existence of normalized solutions for L2-critical constrained problems related to Kirchhoff equations (2014, methodology): “Our method to show the monotonicity of c → γ(c) is quite different from [3,10,26] since no suitable manifold can be used here.”
Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential (2017, methodology): “When V (x) ≡ 0 and N < 4, by almost the same tricks as that of [22], we know that (1.”
Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent (2021, methodology): “On the contrary, we have infu∈Sc Eμ(u) = −∞ for 14 3 < q ≤ 6 or 14 3 < p ≤ 6, and therefore the global minimization method used in [32] does not work any more.”