Sign-Changing Solutions for Discrete Schrödinger Equations with Asymptotically Linear Term

In the present paper, we are interested in the existence of least energy sign-changing solutions for a class of discrete Schrödinger equations involving asymptotically linear behavior. When the linear potentials are assumed to be unbounded at the infinities and the nonlinearities satisfy certain strict conditions, a least energy sign-changing solution has been obtained via constraint variational method, degree theory and deformation lemma. Moreover, the solution changes sign exactly once and has a fast exponential decay with any order, which is firstly obtained by a comparison principle.