Absence of Global Periodic Solutions for a Schrödinger-Type Nonlinear Evolution Equation

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University, Baku, AZ 1148 Azerbaijan

Correspondence to: e-mail: nasibov_sharif@mail.ru

Received 22 June, 2020

Abstract—The problem of the absence of global periodic solutions for a Schrödinger-type nonlinear evolution equation with a linear damping term is investigated. It is proved that when the damping coefficient is nonnegative, the problem does not have global periodic solutions for any initial data, while when it is negative, the same is valid for “sufficiently large values” of the initial data.

Keywords: nonlinear evolution equation, Schrödinger equation, periodic solution, global solution, absence of periodic global solutions

DOI: 10.1134/S1064562420050373