Solutions of perturbed Schrödinger equations with critical nonlinearity

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Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ (2016, methodology): “in RN, (1.2) S.S goes back to the pioneer work [24] by Floer and Weinstein. Since then, it has been studied extensively under various hypotheses on the potential and the nonlinearity, see for example [7, 16, 17, 24, 25, 26, 43, 44, 46, 48] and the references therein. In the study of semiclassical pr”
Singularly perturbed critical Choquard equations (2016, background): “Particularly, the existence and concentration of solutions for local Schrödinger equation with critical exponent was investigated in [1,9,12,38].”
A BERESTYCKI-LIONS THEOREM REVISITED (2012, unknown): “In [15], the lower-order perturbed term P (x)|u|p−2u plays a key role and it is necessary that P (x) cannot be zero.”
Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials (2007, background): “Therefore, we will consider another equivalent problem as in [8,9]: − u + λV (x)u = λg(x,u) (1.”