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.
Coffman, Uniqueness of the ground state solution for ∆u − u + u3 = 0 and a variational characterization of other solutions , Arch
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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.