**Gen-Qiang Wang, Sui Sun Cheng**

## Periodic Solutions of
Higher Order Nonlinear Difference Equations via a Continuation Theorem

**Abstract:**

Based on a continuation theorem of Mawhin, periodic solutions are found for
difference equations of the form

\[\Delta ^{k}y_{n}=f( n,y_{n},y_{n-1},\cdots ,y_{n-l}),\quad n\in Z. \]

**Keywords:**

Periodic solution, difference equation, continuation theorem.

**MSC 2000:** 39A11