(untitled) (Journal of Partial Differential Equations, 2025)
In this paper, we study the following three-dimensional Schrödinger equation with combined Hartree-type and power-type nonlinearities i_tψ+Δψ+(|x|^-2*|ψ|^2)ψ+|ψ|^p-1ψ=0with 1 < p < 5. Using standard variational arguments, the existence of ground state solutions is obtained. And then we prove that when p≥3, the standing wave solution e^ iωtu_ω(x) is strongly unstable for the frequency ω>0.