@article{Wang2022, 
author = {Zhenguo Wang and Yuanxian Hui and Liuyong Pang},
title = {Gap solitons in periodic difference equations with sign-changing saturable nonlinearity},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {18824-18836},
keywords = {Schrödinger equations, gap solitons, critical point theory, approximation},
url = {https://www.sciopen.com/article/10.3934/math.20221036},
doi = {10.3934/math.20221036},
abstract = {In this paper, we consider the existence of gap solitons for a class of difference equations:     L      u          n        −  ω      u          n        =      f          n        (      u          n        )  ,  n  ∈      Z    ,where    L      u          n        =      a          n            u          n      +      1        +      a          n      −      1            u          n      −      1        +      b          n            u          n       is the discrete difference operator in one spatial dimension,    {      a          n        } and    {      b          n        } are real valued T-periodic sequences,    ω  ∈      R  ,        f          n        (  ⋅  )  ∈  C  (      R    ,      R    ) and        f          n      +      T        (  ⋅  )  =      f          n        (  ⋅  ) for each    n  ∈      Z  . Under general asymptotically linear conditions on the nonlinearity        f          n        (  ⋅  ), we establish the existence of gap solitons for the above equation via variational methods when    t      f          n        (  t  ) is allowed to be sign-changing. Our methods further extend and improve the existing results.}
}