Abstract
We consider the higher order diffusion Schrodinger equation with a time nonlocal nonlinearity
i partial derivative(t)u - (-Delta(H))(m)u = lambda/Gamma(alpha) integral(t)(0) (t - s)(alpha-1)vertical bar u(s)vertical bar(p) ds,
posed in (eta, t) is an element of H x (0, + infinity), supplemented with an initial data u(eta, 0) = f (eta), where m > 1, p > 1, < alpha < 1, and Delta(H) is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group H. Then, we prove a blow up result for its solutions. Furthermore, we give an upper bound estimate of the life span of blow up solutions.