Normalized ground states for the NLS equation with combined nonlinearities

We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities−Δu=λu+μ|u|q−2u+|u|p−2uin RN, N≥1, having prescribed mass∫RN|u|2=a2. Under different assumptions on q0 and μ∈R we prove several existence and stability/instability results. In particular, we consider cases when2