Strong instability of standing waves for the divergence Schrödinger equation with inhomogeneous nonlinearity

Abstract

This paper considers a class of Schrödinger type equations with a divergence dispersive term and inhomogeneous nonlinearity. We first establish the variational characterization of ground states by introducing a weighted Sobolev embedding theorem. Then, based on a localized variance-type estimate, we prove that the standing waves are strongly unstable using blow-up.