Asymptotically polynomial solutions of difference equations

作者：Migda Janusz^*

来源：Advances in Difference Equations, 2013, 2013(1): 1-16.

DOI：10.1186/1687-1847-2013-92

• difference equation
• asymptotically polynomial solution
• prescribed asymptotic behavior

Asymptotic properties of solutions of a difference equation of the form %26lt;br%26gt;Delta(m)x(n)=a(n)f(n, x(sigma(n)))+b(n) %26lt;br%26gt;are studied. We present sufficient conditions under which, for any polynomial phi(n) of degree at most m-1 and for any real s %26lt;= 0, there exists a solution x of the above equation such that x(n) = phi(n)+o(n(s)). We give also sufficient conditions under which, for given real s %26lt;= m-1, all solutions x of the equation satisfy the condition x(n) = phi(n)+o(n(s)) for some polynomial phi(n) of degree at most m-1.

• 出版日期2013