A positive solution for a nonlinear Schrödinger equation on Rn

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An existence and stability result for standing waves of nonlinear Schrödinger equations (2006, background): “See nevertheless [16] for an existence result under general conditions on g but for a restricted class of potentials V .”
Ground states of nonlinear Schrödinger equations with potentials (2006, methodology): “1; but the conditions in [5] and ours are mutually non-inclusive and the methods are different.”
The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, unknown): “In [41], Teng adapted the monotonicity trick (see for example, Jeanjean and Tanaka [24]) to obtain the existence of ground state solutions to ⎧ ⎨ ⎩ (− )su + V (x)u + φu = μ|u|q−1u + |u|2∗s−2u, in R3, (− )tφ = αu2, in R3, for q ∈ (2, 2∗s − 1).”
Positive and Nodal Solutions For a Nonlinear Schrödinger Equation with Indefinite Potential (2008, background): “Several new results concerning sign changing potentials V have appeared lately (e.g. [24, 11, 13, 15, 16, 17 ]).”
Berestycki-Lions conditions on ground state solutions for a Nonlinear Schrödinger equation with variable potentials (2018, methodology): “[4] Assume that (V1), (V2) and (F1)-(F3) hold.”