\(l^p\) Solution to the Initial Value Problem of the Discrete Nonlinear Schrödinger Equation with Complex Potential

In this paper we study the time-dependent discrete nonlinear Schrödinger equation with complex, not necessarily bounded potential and sufficiently general nonlinearity on a multidimensional lattice with a weighted \(l^p\) initial value. Under natural assumptions, we prove the global well-posedness in weighted \(l^p\) spaces.