Solutions for a quasilinear Schr"odinger equation: a dual approach

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Quasilinear elliptic equations via perturbation method (2012, methodology): “…the ﬁrst attempt in this direction, though for the special form of equations (1), multiplicity results could be derived by using the change of variable arguments from [7, 11] (we refer to recent work [1, 8, 17] for more references on using the arguments of changing variables for various problems).”
Multiple Sign-Changing Solutions for Quasilinear Elliptic Equations via Perturbation Method (2014, methodology): “While the methods in [10, 22] is most effective it works only for the special form of the quasilinear term.”
Existence of infinitely solutions for a modified nonlinear Schrödinger equation via dual approach (2018, background): “In addition, since G−1 is an odd function, (G5) and (G11) are consequences of (G3) and (G4), moreover (G7) is also consequence of [4, 5].”
Uniqueness (2021, unknown): “To treat u Δ u 2 , a substitution u = f ( v ) (cf. (8.2)) was introduced in [28, 59], which reduced (8.1) to a semilinear equation, with a more complicated nonlinear zero order term.”
Quasilinear elliptic equations with critical growth via perturbation method (2013, methodology): “This idea was initially used in [10,23] for existence of solutions of subcritical problems.”