Scattering for nonradial 3D NLS with combined nonlinearities: the interaction Morawetz approach (Q6540276)

This work addresses the problem of scattering in a 3D system stated by the nonlinear Schrödinger equation, where the nonlinear part is balanced by the combination of focusing and defocusing terms \(|u|^ {q-1} - |u|^{p-1}\). As a result, it is proven that there are possible two outcomes: (i) in the case \(7/3 < q < p < 5\), the corresponding solution exists globally for positive wave frequencies for the initial conditions corresponding to the positive Pohozaev functional, (ii) a blowing up in finite time solution when the initial condition corresponds to the positive Pohozaev functional.