Reverse-Order Lower and Upper Functions for Periodic Problems of Second-Order Singular Difference Equations

Abstract EN

We present sufficient conditions ensuring the lower and upper functions on the reversed-order for the periodic difference equations.

This enables us to obtain the existence of positive periodic solutions of the second-order difference equation Δ2u(t-1)=g(t)/uμ(t)-h(t)/uλ(t)+f(t), t∈ℤ, where g,h:ℤ→[0,∞), and f:ℤ→ℝ are T-periodic functions, λ,μ>0.