Discrete nonlinear Schrödinger equations with superlinear nonlinearities

In this paper, we study the discrete nonlinear equation.Lun-ωun=σχngn(un),n∈Z,where ω belongs to a finite spectral gap of the operator L or it is a lower edge of a finite spectral gap. By using a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou, we will study the existence of nontrivial solitons for this equation with gn is super linear.