Abstract

We prove the existence of orbitally stable standing waves with prescribed L ²-norm for the following Schrödinger-Poisson type equation
[...]
when p ε {8/3} U(3, 10/3). In the case 3 < p < 10/3, we prove the existence and stability only for sufficiently large L ²-norm. In case p=8/3, our approach recovers the result of Sanchez and Soler (J. Stat. Phys. 114:179–204, 2004) for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In the final section, a further application to the Schrödinger equation involving the biharmonic operator is given.

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