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.