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

Abstract

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

Keywords

• Positive periodic solutions
• existence
• nonexistence
• difference equations
• fixed point