Abstract
This notes studies the inhomogeneous non-linear Schrodinger equations with a harmonic potentiali partial differential
i partial derivative(t)u + Delta u - vertical bar x vertical bar(2)u + vertical bar x vertical bar(b)vertical bar u vertical bar(p-1) u = 0.
Indeed, following the methods of Fukuizumi and Ohta (Differ Integral Equ 16(6):691-706, 2003), Ohta (Funccialaj Ekvacioj 61:135-143, 2018), the non-linear and strong instability of standing waves are obtained in the two different regimes b > 0.