SOLITON AND BLOW-UP SOLUTIONS TO THE TIME-DEPENDENT SCHRODINGER-HARTREE EQUATION

We study the Cauchy problem for the focusing time-dependent Schrodinger - Hartree equation i partial derivative(t)psi + Delta psi = -(vertical bar x vertical bar(-(n-2)) * vertical bar psi vertical bar(alpha))vertical bar psi vertical bar(alpha-2)psi, alpha >= 2, for space dimension n >= 3. We prove the existence of solitary wave solutions and give conditions for formation of singularities in dependence of the values of alpha >= 2 and the initial data psi(0, x) =psi(0)(x).