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math.AP2011★ 265 cited
Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
Jacopo Bellazzini, Louis Jeanjean, Tingjian Luo
In this paper we study the existence and the instability of standing waves with prescribed -norm for a class of Schrödinger-Poisson-Slater equations in %orbitally sta…
math-ph2011★ 10 cited
Ground states for semi-relativistic Schrödinger-Poisson-Slater energies
Jacopo Bellazzini, Tohru Ozawa, Nicola Visciglia
We prove the existence of ground states for the semi-relativistic Schrödinger-Poisson-Slater energy $$I^{α,β}(ρ)=\inf_{\substack{u\in H^\frac 12(\R^3) \int_{\R^3}|u|^2 dx=ρ}} \frac…