We study a higher order difference equation. By Lyapunov-Schmidt reduction methods and computations of critical groups, we prove that the equation has four -periodic solutions.
Ronghui Hu. "Multiplicity of Periodic Solutions for a Higher Order Difference Equation." Abstr. Appl. Anal. 2014 (SI18) 1 - 7, 2014. https://doi.org/10.1155/2014/925290