J. Nonl. Evol. Equ. Appl. 2024 (1), pp. 1-17, published on April 23, 2024:

p-Solution to the Initial Value Problem of the Discrete Nonlinear Schrödinger Equation with Complex Potential, II

Guoping Zhang and Ghder Aburamyah

Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

Received on October 3, 2023,
Accepted on January 20, 2024

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper, we prove the global well-posedness of the initial value problem of the time-dependent discrete nonlinear Schrödinger equation with a complex potential and sufficiently general nonlinearity on a multidimensional lattice in weighted ℓp spaces in the case 2
Keywords: Discrete nonlinear Schrödinger equation, semigroup, initial value problem, Lipschitz continuous, complex potential, ℓp solution.
2010 Mathematics Subject Classification:   37L60, 35B41, 35Q55.

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