Standing waves with a critical frequency for nonlinear Schrödinger equations, II

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Singular elliptic problems with lack of compactness (2005, background): “Notice that equations of this type come from the consideration of standing waves in anisotropic Schrödinger equations (see [2, 20, 21, 25]).”
Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases (2008, methodology): “This type of penalization was first introduced in [9].”
Sum of weighted Lebesgue spaces and nonlinear elliptic equations (2011, background): “a particular critical frequency case, as termed in [23, 24 ]).”
Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “studied recently (e.g., [1, 3, 4, 5, 6, 8, 9 , 10, 11, 12, 18, 19, 20, 24, 25, 26])”
Bound states for semilinear Schrödinger equations with sign-changing potential (2007, background): “A problem similar to (1.2) has been considered by Bartsch, Pankov and Wang [4], and Liu, van Heerden and Wang [14].”
Semi-classical states for the Choquard equation (2013, methodology): “This penalization scheme should not be confused with the global penalization scheme of J. Byeon and Z.-Q. Wang which penalizes globally the L 2 norm outside a concentration [15,17,19].”