Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 12, pp. 1-19.

Title: Global attractor and l^p solutions to initial value problems of
 discrete nonlinear Schrodinger equations complex potential
       
Authors: Guoping Zhang   (Morgan State Univ., Baltimore, MD, USA)
         Ghder Aburamyah (Morgan State Univ., Baltimore, MD, USA)

Abstract:
In this article, we investigate the global well-posedness of
initial value problems of the time-dependent discrete nonlinear Schrodinger equation
with a complex potential and sufficiently general nonlinearity on a multidimensional
lattice in weighted $\elll^p$ spaces for $1<p<\infty$.
Thanks to our improved estimates we are able to prove the existence of global
attractor for $\ell^p$ solutions to the initial value problem.  

Submitted November 1, 2023. Published January 31, 2024.
Math Subject Classifications: 37L60, 35B41, 35Q55.
Key Words: Discrete nonlinear Schrodinger equation; semigroup; l^p solution;
   global attractor; Lipschitz continuous; initial value problem; complex potential.