Breather solutions of the discrete nonlinear Schroedinger equations with sign changing nonlinearity

In this paper, we investigate the breather solutions of the discrete nonlinear Schroedinger equation with the unbounded potential and nonlinearity containing both self-focusing and defocusing sites (which means the coefficients of nonlinearity change sign). By using the generalized Nehari manifold method, we obtain the existence of nontrivial exponential decay breather solutions.