BLOW-UP FOR THE FOCUSING ENERGY CRITICAL NONLINEAR SCHRODINGER EQUATION WITH CONFINING HARMONIC POTENTIAL

The focusing nonlinear Schrodinger equation (NLS) with confining harmonic potential i partial derivative(t)u + 1/2 Delta u - 1/2 vertical bar u vertical bar(4/(d -2))u, x is an element of R-d, is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.