Ground states of the degenerate nonlinear elliptic equation are radially symmetric, unique, and non-degenerate in the radial Sobolev space.
Ichinose:The Cauchy problem for Schrödinger type equations with variable coefficients, Osaka J
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Radial symmetry, uniqueness and non-degeneracy of solutions to degenerate nonlinear Schr\"odinger equations
Ground states of the degenerate nonlinear elliptic equation are radially symmetric, unique, and non-degenerate in the radial Sobolev space.