The regularity properties and blow-up of the solutions for nonlocal Schrödinger equations.

In this paper, the Cauchy problem for convolution-type nonlocal linear and nonlinear Schrödinger equations (NSEs) is studied. The equations include the general differential operators. The existence, uniqueness, Lp-regularity properties of linear problem and the existence, uniqueness, and blow-up at finite time of the nonlinear problem are obtained. By choosing differential operators including in equations, the regularity properties of a different type of nonlocal Schrödinger equation are studied. [ABSTRACT FROM AUTHOR]