Abstract
We consider a higher order functional difference equations on \({\mathbb Z}\) with an eigenvalue parameter \(\lambda \) in the equation. Sufficient conditions are obtained for the existence of at least one or two positive periodic solutions of the equation for different values of \(\lambda \). The nonlinear function in the equation is allowed to be sign-changing in some of our results. Our proofs utilize Krasnosel’skii’s fixed point theorem.
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Acknowledgments
The research by Jacob D. Johnson, Michael G. Ruddy, and Alexander M. Ruys de Perez was conducted as part of a 2013 Research Experience for Undergraduates at the University of Tennessee at Chattanooga that was supported by NSF Grant DMS-1261308.
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Johnson, J.D., Kong, L., Ruddy, M.G. et al. Positive Periodic Solutions for a Higher Order Functional Difference Equation. Differ Equ Dyn Syst 23, 195–208 (2015). https://doi.org/10.1007/s12591-013-0192-4
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DOI: https://doi.org/10.1007/s12591-013-0192-4