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

Abstract This paper studies the orbital instability of standing waves for the Klein–Gordon–Schrodinger 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.