Global attractor and l^p solutions to initial value problems of discrete nonlinear Schrodinger equations complex potential

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 \( l^p\) spaces for \( 1< p <\infty\). Thanks to our improved estimates we are able to prove the existence of global attractor for \( l^p\) solutions to the initial value problem. For more information see https://ejde.math.txstate.edu/Volumes/2024/12/abstr.html