Electron. J. Differential Equations, Vol. 2024 (2024), No. 12, pp. 1-19.

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

Guoping Zhang, Ghder Aburamyah

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.

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.
DOI: 10.58997/ejde.2024.12

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Guoping Zhang
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: guouping.zhang@morgan.edu
  Ghder Aburamyah
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: ghabu2@morgan.edu

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