Asymptotic behavior results for nonlinear neutral delay difference equations

作者：Wei; Gengping

来源：Applied Mathematics and Computation, 2011, 217(17): 7184-7190.

DOI：10.1016/j.amc.2011.02.004

• Neutral delay difference equation
• Boundedness
• Asymptotic behavior
• Liapunov functional

This paper is concerned with the nonlinear neutral delay difference equation
Delta[x(n) - c(n)x(n - m)] + p(n)f(x(n - k)) = 0; n is an element of N(n(0)), (*)
where Delta is the forward difference operator defined by Delta x(n) = x(n + 1) - x(n), {c(n)} is a sequence of real numbers, {p(n)} is a positive sequence, f is an element of C(R, R), m and k are positive integers, n(0) is a nonnegative integer and N(n(0)) = {n(0), n(0) + 1, n(0) + 2,...}. Sufficient conditions are obtained under which every solution of equation (*) is bounded and tends to a constant as n -> infinity. Our results improve and extend some known results. One example is given to illustrate our results.

• 出版日期2011-5-1
• 单位怀化学院