Orbital instability of standing waves for the Klein-Gordon-Schrödinger system with quadratic-cubic nonlinearity

This paper studies the orbital instability of standing waves for the Klein-Gordon-Schrödinger system in three space dimensions. By variational methods we first show the existence of ground states. Then we establish a Virial identity for this system, by which and a Virial theorem, we manage to prove that the standing waves we obtained are orbital instable as if the frequency ω is sufficiently small. Our results improve and complement some previous ones.