Convergence of the positive solutions of a nonlinear neutral difference equation

Abstract

Sufficient conditions are established that guarantee the convergence of the positive solutions of a neutral-type difference equation of the form $$ \Delta [x(n) - q(n)x(\sigma (n))] + p(n)f(x({\tau_1}(n)), \ldots, x({\tau_k}(n))) = 0, $$ where σ(n); n = 1, 2, …, are retarded arguments and τ j (n) j = 1, …, k, are general deviated arguments.