Abstract
In this paper, we study the existence of nonnegative solutions for the parabolic problem... u + Vu + 2... u -. u. t = 0, in D x ( 0,+8),.( x) u( x, t) = 0, ( x, t).. D x ( 0,+8), u( x, 0) = u0( x), x. D, where D is a smooth domain of Rn, ( n = 3), the function u0 is such that.u0. L2( D) and. is the normalized positive eigenfunction corresponding to the first eigenvalue of - and V belongs to a class of time- dependant potentials which can be written as a nonlinear combination of derivatives of a function.