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| For a quasilinear Schrodinger equation arising in Plasma Physics we prove the existence of two solutions having a prescribed $L^2$ norm. These solutions are obtained as constrained critical points of the associated functional. One of these solutions is a mountain pass solution relative to the constraint and the other one a minimum either local or global. The orbital stability/instability of the associated standing waves, which is widely open, will also be discussed. |
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