Existence of the Local Solution of a Non Homogeneous Schrödinger Type Equation - Ayala, Yolanda Silvia Santiago (European Journal of Applied Sciences, 2024)
In this article, we prove that initial value problem associated to the Schrödinger type non homogeneous equation in periodic Sobolev spaces has a local solution in [0, T] with T > 0, and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem. We do this in a intuitive way using Fourier theory and introducing a Co- group inspired by the work of Iorio [1] and Santiago [7]. Also, we prove the uniqueness solution of the Schrödinger type homogeneous equation, using its conservative property, inspired by the work of Iorio [1] and Santiago [6]. Finally, we study its generalization to n-th order equation.