Blow-up solutions for a class of divergence Schrödinger equations with intercritical inhomogeneous nonlinearity

In this article, we study a class of divergence Schrödinger equations with intercritical inhomogeneous nonlinearity $i∂tu+∇⋅(|x|b∇u)=−|x|c|u|pu,(x,t)∈Rn×R,$ where 2 − n < b < 2, c ≥ b − 2, and 2(2 − b) − bp < np − 2c < (2 − b)(p + 2). We prove the blow-up of radial solutions for the negative energy by using a virial-type estimate. In addition, we derive a generalized Gagliardo–Nirenberg inequality and use it to establish the general blow-up criteria for radial solutions with non-negative energy.