Proves ground state existence, symmetry, uniqueness, instability and scattering/blow-up dichotomy for NLS with competing inhomogeneous nonlinearities in the non-radial inter-critical regime.
Yanagida, Uniqueness of positive radial solutions of ∆u+f (u, |x|) = 0, Nonlinear Anal., 19 (1992), 1143–1154
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NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
Proves ground state existence, symmetry, uniqueness, instability and scattering/blow-up dichotomy for NLS with competing inhomogeneous nonlinearities in the non-radial inter-critical regime.