  We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential
in the presence of two combined energy-subcritical power nonlinearities. We
assume that the larger power is defocusing, and the smaller power is focusing.
Such a framework includes physical models, and ensures that finite energy
solutions are global in time. We address the questions of the existence and the
orbital stability of the set of standing waves. Given the mathematical features
of the equation (external potential and inhomogeneous nonlinearity), the set of
parameters for which standing waves exist in unclear. In the twodimensional
case, we adapt the method of fundamental frequency solutions, introduced by the
second author in the higher dimensional case without potential. This makes it
possible to describe accurately the set of fundamental frequency standing waves
and ground states, and to prove its orbital stability.
