Threshold scattering for the focusing NLS with a repulsive Dirac delta potential

We establish the scattering of solutions to the focusing mass supercritical nonlinear Schrodinger equation with a repulsive Dirac delta potential i partial derivative(t)u+ partial derivative(2)(x)u + gamma delta(x)u + vertical bar u vertical bar(p-1)u = 0, (t, x) is an element of R x R, at the mass-energy threshold, namely, when E-gamma(u(0))[M(u(0))](sigma)= E-0(Q)[M(Q)](sigma) where u(0) is an element of H-1(R) is the initial data, Q is the ground state of the free NLS on the real line R, E-gamma is the energy, M is the mass and sigma = (p+3)/(p-5). We also prove failure of the uniform space-time bounds at the mass-energy threshold. (c) 2021 Elsevier Inc. All rights reserved.