| Abstract: |
| We consider the ground states for Schroedinger equation with mixed power non-linearities in any spatial dimension. The question for the stability of these waves, in spatial dimension one, is well-understood and depends on a sign of a (hard) integral.
In higher spatial dimensions however, there are few results, even for two different powers, as the equation suffers a loss of homogeneity. We provide a variational construction of some of these waves (note that we even allow focusing and defocusing powers). As a consequence, we show their spectral stability and in the case of two powers, their orbital stability as well. |
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