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We prove the existence of normalized ground state solutions for thebiharmonic Schr\"odinger equation with combined nonlinearities and show thatall ground states correspond to the local minima of the associated energyfunctional restricted to the appropriate set. Moreover, we prove that thestanding waves are strongly unstable by blowup. In particular, our resultscover the critical case. Our method is novel and innovative as previous ideascannot be used in many cases under this study.

Existence and instability of standing waves for the biharmonic nonlinear Schroedinger equation with combined nonlinearities