Positive periodic solutions of functional discrete systems with a parameter
The existence of multiple positive periodic solutions of the system of difference equations with a parameter
x(n + 1) = A(n, x(n))x(n) + λf(n, xn),
is studied. In particular, we use the eigenvalue problems of completely continuous operators to obtain our results. We apply our results to a well-known model in population dynamics.
 Y. Chen, B. Dai and N. Zhang, Positive periodic solutions of non-autonomous functional differential systems, J. Math. Anal. Appl. 333 (2007) 667-678.
 S. N. Elaydi, An Introduction to Difference Equations, 2nd ed., Undergraduate Texts in Math- ematics, Springer-Verlag, New York, 1999.
 D.J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics and Science and Engineering, vol. 5, Academic Press Inc., Boston, MA, 1988, pp. 2-99.
 J. Henderson and A. Peterson, Properties of delay variation in solutions of delay difference equations, Journal of Differential Equations, 1 (1995), 29-38.
 R.P. Agarwal and P.J.Y. Wong, On the existence of positive solutions of higher order difference equations, Topological Methods in Nonlinear Analysis, 10 (1997) 2, 339-351.
 P.W. Eloe, Y. Raffoul, D. Reid and K. Yin, Positive solutions of nonlinear Functional Difference Equations, Computers and Mathematics With applications, 42 (2001) , 639-646.
 J. Henderson and W. N. Hudson, Eigenvalue problems for nonlinear differential equations, Communications on Applied Nonlinear Analysis, 3 (1996), 51-58.
 M. A. Krasnosel’skii, Positive solutions of operator Equations, Noordhoff, Groningen, (1964).
 Y. Li and L. Zhu, Positive periodic solutions of higher-dimensional functional difference equations with a parameter, J. Math. Anal. Appl. 290 (2004) 654-664.
 F. Merdivenci, Two positive solutions of a boundary value problem for difference equations, Journal of Difference Equations and Application, 1 (1995), 263-270.
 Y.N. Raffoul, Positive periodic solutions of nonlinear functional difference equations, Electron. J. Differential Equations, 55 (2002) 1-8.
 Y.N. Raffoul, Periodic solutions for scalar and vector nonlinear difference equations, Pan- American Journal of Mathematics, 9 (1999), 97-111.
 W. Yin, Eigenvalue problems for functional differential equations, Journal of Nonlinear Differential Equations, 3 (1997), 74-82.