Periodic Solutions in Shifts δ± for a Nonlinear Dynamic Equation on Time Scales

Abstract EN

Let ?⊂ℝ be a periodic time scale in shifts δ±.

We use a fixed point theorem due to Krasnosel'skiĭ to show that nonlinear delay in dynamic equations of the form xΔ(t)=-a(t)xσ(t)+b(t)xΔ(δ-(k,t))δ-Δ(k,t)+q(t,x(t),x(δ-(k,t))),t∈?, has a periodic solution in shifts δ±.

We extend and unify periodic differential, difference, h-difference, and q-difference equations and more by a new periodicity concept on time scales.