Abstract
In this paper, we study the initial value problem for the nonlocal in time nonlinear Schrodinger equation
iu(t) + Delta u = lambda J(0)(vertical bar t)(alpha)vertical bar mu vertical bar(p), x is an element of R-N, t > 0,
u(x, 0) = f(x), x is an element of R-N.
Using the test function method, we derive a blow-up exponent. Then based on integral inequalities, we estimate the life span of blowing-up solutions.