In this paper we study the time-dependent discrete nonlinear Schrödinger equation with complex, not necessarily bounded, potential and sufficiently general nonlinearity on a multi dimensional lattice. Under natural assumptions we prove the global well-posedness in weighted $l^2$ spaces. In the dissipative case we obtain a result on the existence of global compact attractor in such spaces.

中文翻译：

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具有复势的离散非线性薛定谔方程的初值问题

在本文中，我们研究了多维晶格上具有复杂的、不一定有界的、潜在的和足够一般的非线性的时间相关离散非线性薛定谔方程。在自然假设下，我们证明了加权的全局适定性$l^2$空格。在耗散的情况下，我们得到了在这样的空间中存在全局紧致吸引子的结果。