Electron. J. Diff. Equ., Vol. 2011 (2011), No. 96, pp. 1-9.

Positive periodic solutions of nonlinear first-order functional difference equations with a parameter

Yanqiong Lu

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.

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Yanqiong Lu
Department of Mathematics
Northwest Normal University
Lanzhou, 730070, China
email: linmu8610@163.com

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