Positive solutions to a class of quasilinear elliptic equations on $\mathbb R$

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We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on $\mathbb R$.

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Quasilinear elliptic equations with critical growth via perturbation method (2013, unknown): “Define the mountain pass value for the functional I+ μ which is defined by replacing u by u+ in F (u) of the definition of Iμ c+(μ)= inf γ∈Γ sup t∈[0,1] I+ μ ( γ (t) ) , Γ = {γ ∈ C([0,1], X) ∣∣ γ (0)= 0, I+ μ(γ (1))< 0}.”
Multiple normalized solutions for quasi-linear Schr\"odinger equations (2014, background): “3] (see also [4]).”
Soliton solutions for quasilinear Schrödinger equations with critical growth (2010, unknown): “[2] A.”