Localization of Fučík curves for the second order discrete Dirichlet operator

In this paper, we deal with the second order difference equation asymmetric nonlinearities on integer lattice and investigate distribution of zeros for continuous extensions positive semi-waves. The distance between two consecutive different semi-waves depends not only parameters problem but also position one these respect to lattice. We provide an explicit formula distance, which allows us obtain a new simple implicit description all non-trivial Fučík curves discrete Dirichlet operator. Moreover, fixed problem, show that is bounded attains its global extrema are explicitly described in terms Chebyshev polynomials kind. Finally, each curve, suitable bounds by similar first curve.