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 lp spaces for 1<p<∞. Thanks to our improved estimates we are able to prove the existence of global attractor for lp 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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