Ground state in the energy super-critical Gross–Pitaevskii equation with a harmonic potential

The energy super-critical Gross–Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d ? 5 . In order to prove existence ground state (a positive, radially symmetric solution space), we develop shooting method deal one-parameter family classical solutions an initial-value problem for stationary equation. We that curve (the graph eigenvalue parameter versus supremum norm) oscillatory ? 12 monotone 13 Compared existing literature, rigorous asymptotics are derived by constructing three families functional-analytic rather than geometric methods.