Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrodinger equations with growing potentials

In this paper, we consider the following equation: i partial derivative u/partial derivative t +Delta u+g(x)|u|(4/N)u- Wu= 0. We construct a critical-mass solution that blows up at a finite time and describe the behaviour of the solution in the neighbourhood of the blow-up time. Banica-Carles-Duyckaerts (2011) have shown the existence of a critical-mass blow-up solution under the assumptions that N <= 2, that g and W are sufficiently smooth and that each derivative of these is bounded. In this paper, we show the existence of a critical-mass blow-up solution under weaker assumptions regarding smoothness and boundedness of g and W. In particular, it includes the cases where W is unbounded at spatial infinity or not Lipschitz continuous.