Asymptotic behavior results for solutions to some nonlinear difference equations

作者：Jamieson William T; Merino Orlando^*

来源：Journal of Mathematical Analysis and Applications, 2015, 430(2): 614-632.

DOI：10.1016/j.jmaa.2015.04.094

• Vector difference equation
• Poincare equation
• Asymptotic behavior
• Convergent solutions

We give asymptotic results for convergent solutions {x(n)} of (real or complex) difference equations x(n+1) = J x(n)+f(n)(x(n),), where x(n) is an m-vector, J is a constant m x m matrix and f(n)(y) is a vector valued function which is continuous in y for fixed n, and where f(n)(y) is small in a sense. In addition, we obtain asymptotic results for solutions {x(n)} of the Poincare difference equation x(n+1) = (A + B-n)x(n) where B-n satisfies parallel to B-n parallel to = O(eta(n)) with eta is an element of (0,1). An application illustrates the results.

• 出版日期2015-10-15