Morse index for the ground state in the energy supercritical Gross–Pitaevskii equation

The ground state of the energy super-critical Gross–Pitaevskii equation with a harmonic potential converges in space to singular solution limit large amplitudes. can be represented by curve which has either oscillatory or monotone behavior, depending on dimension system and power focusing nonlinearity. We address here case for cubic nonlinearity spatial dimensions d≥13. By using shooting method radial Schrödinger operators, we prove that Morse index is finite independent (large) amplitude. also it equal limiting solution, computed from numerical approximations. results suggest one every