The Cauchy problem for nonlocal abstract Schrödinger equations and applications

Here, the Cauchy problem for linear and nonlinear nonlocal Schrödinger equations are studied. The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform are operator functions defined in a Hilbert space H together with some growth conditions. By assuming enough smoothness on the initial data and the operator functions, the local and global existence and uniqueness of solutions are established. We can obtain a different classes of nonlocal Schr ödinger equations by choosing the space H and linear operators, which occur in a wide variety of physical systems