Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 96, pp. 1-9.

Title: Positive periodic solutions of nonlinear first-order functional
       difference equations with a parameter
       
Author: Yanqiong Lu (Northwest Normal Univ., Lanzhou, China)

Abstract:
 We obtain the existence and multiplicity of positive
 $T$-periodic solutions for the difference equations
 $$
 \Delta x(n)=a(n,x(n))-\lambda b(n)f(x(n-\tau(n)))
 $$
 and
 $$
 \Delta x(n)+a(n,x(n))=\lambda b(n)f(x(n-\tau(n))),
 $$
 where $f(\cdot)$ may be singular at $x=0$.
 Using a fixed point theorem in cones, we extend recent results
 in the literature.

Submitted June 29, 2011. Published July 28, 2011.
Math Subject Classifications: 34G20.
Key Words: Positive periodic solutions; existence; nonexistence;
           difference equations; fixed point.