Gaetano Siciliano

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In this paper we consider the stationary solutions of the Schrödinger-Poisson equation: iψt +∆ψ − (|x| ∗ |ψ|)ψ + |ψ|ψ = 0 in R. We are interested in the existence of standing waves, that is solutions of type ψ(x, t) = u(x)e−iωt, where ω ∈ R, with fixed L − norm. Then we are reduced to a constrained minimization problem. The main difficulty is the(More)
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