Spherical semiclassical states of a critical frequency for Schrodinger equations with decaying potentials

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Sum of weighted Lebesgue spaces and nonlinear elliptic equations (2011, background): “[10,12,22,25,26,37] and [1,3,21,31,37] respectively, and the references therein), showing essentially that the existence of solutions relies on suitable compatibility conditions between the power of u and the growth and decaying rates of V (x) (and possibly of the nonlinearity) at zero and infinity.”
Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “These type equations have been studied recently (e.g., [1] [3] [4] [5] [6] [8] [9] [10] [11] [12] [18] [19] [20] [24] [25] [26]) (1.1) −∆u + V (x)u = f (x, u) where the dependence on x can tend to infinity or zero somewhere.”