Journal of Dynamics and Differential Equations

, Volume 18, Issue 4, pp 943–960

Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

Authors

  • Zhiming Guo
    • College of Mathematics and Information SciencesGuangzhou University
    • College of Mathematics and Information SciencesGuangzhou University
Article

DOI: 10.1007/s10884-006-9042-1

Cite this article as:
Guo, Z. & Yu, J. J Dyn Diff Equat (2006) 18: 943. doi:10.1007/s10884-006-9042-1

Abstract

By using the Zp geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations
$$\Delta^2x_{n-1}+f(x_n)=0$$
are obtained. By two examples, we show that our results are the best possible in the sense that the lower bound of the number of periodic solutions cannot be improved.

Keywords

Second-order difference equationsperiodic solutioncritical pointZp index theory

Mathematics Subject Classification

39A11

Copyright information

© Springer Science+Business Media, Inc. 2006