Convergence and Divergence of the Solutions of a Neutral Difference Equation

[摘要] We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the formΔ[x(n)+cx(τ(n))]+p(n)x(σ(n))=0, whereτ(n)is a general retarded argument,σ(n)is a general deviated argument (retarded or advanced),c∈ℝ,(p(n))n≥0is a sequence of positive real numbers such thatp(n)≥p,p∈ℝ+, andΔdenotes the forward difference operatorΔx(n)=x(n+1)−x(n). Also, we examine the asymptotic behavior of the solutions in case they arecontinuous and differentiable with respect toc.

[学科分类] 应用数学