On the Boundedness of the Schrödinger type Differential Equation with Time Involution

In the present paper, the initial value problem for the Schrödinger type involutory partial differential equation is studied. Applying Green's function of space operator, we get formula for solution of this problem. In applications, the theorem on stability of this problem is established. Furthermore, this formula is applied to the existence and uniqueness of bounded solution of nonlinear problem with involution. © 2021 American Institute of Physics Inc.. All rights reserved.