Instability of Solitary Waves for the Generalized Klein–Gordon–Hartree Equation.

In the present paper we show that the ground state standing waves eiωt u(x) for the generalized Klein–Gordon–Hartree equation ψtt−Δψ+ψ−(|x|−(n−α)*|ψ|p)|ψ|p−2ψ=0,α∈(0,n),n≥3 in ℝn, are orbitally unstable in the domain of all frequencies 0 ≤ ω < 1 for the supercritical case and for frequencies, strictly less than a critical frequency ωc=√p−1/n+α+1−p(n−1), in the subcritical case. [ABSTRACT FROM AUTHOR]