Abstract
We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in H1(Rd) and then utilize the concentration–compactness method to show the global wellposedness and scattering versus blowup in H1(Rd) below the threshold for radial data when d≤4.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have