@article{Maroncelli2026, 
author = {Daniel Maroncelli},
title = {On the solvability of the discrete nonlinear Schrödinger equation with subcubic potential},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {4803-4811},
keywords = {Schrödinger's equation, superlinear potentials, subcubic potentials, discrete boundary value problems, periodic solutions},
url = {https://www.sciopen.com/article/10.3934/era.2026212},
doi = {10.3934/era.2026212},
abstract = {In this paper, we analyze the solvability of the discrete nonlinear Schrödinger equation     i  β  (      Δ    t    +      ∇    t    )  φ  (  t  ,  k  )  +  γ      |    φ  (  t  ,  k  )            |        2    φ  (  t  ,  k  )  +  ε      Δ    k    2    φ  (  t  ,  k  −  1  )  =  g  (  t  ,  φ  (  t  ,  k  )  )  ,where        Δ    t   and        Δ    k   denote the standard forward difference operators in the variables    t and    k, respectively,        ∇    t   denotes the standard backward difference operator in    t, and         Δ    k    2    φ  (  t  ,  k  −  1  )  =  φ  (  t  ,  k  +  1  )  −  2  φ  (  t  ,  k  )  +  φ  (  t  ,  k  −  1  )is the discrete Laplacian operator in the spatial variable    k. Throughout, we will assume the parameters    β and    ε are positive real numbers, the parameter    γ is a nonzero real number, and the potential function    g  :      Z    ×      C    →      C   is continuous.}
}