Lifshits tails for random Schrodinger operators with nonsign definite potentials

This paper is devoted to the study of Lifshits tails for random Schrodinger operator acting on L-2(R-d) of the form H-lambda,H-w = H-0 + lambda Sigma(gamma is an element of Zd) w(gamma)tau V-gamma, where H-0 is a Z(d)-periodic Schrodinger operator, lambda is a positive coupling constant, (w(gamma))(gamma is an element of Zd) are i.i.d and bounded random variables and V is the single site potential with changing sign. We prove that, in the weak disorder regime, at an open band edge, a true Lifshits tail for the random Schrodinger operator occurs under a certain set of conditions on H-0 and on V.