Global Existence and Long-Term Behavior of a Nonlinear Schrödinger-Type Equation

Abstract

We study a global mixed problem for the nonlinear Schrödinger equation with a nonlinear term in which the coefficient is a generalized function. A global solvability theorem for the analyzed problem is proved by using the general solvability theorem from [K. N. Soltanov, Nonlin. Anal.: Theory, Meth., Appl., 72, No. 1 (2010)]. We also investigate the behavior of the solution of the problem under consideration.