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

Erbil Çetin and F. Serap Topal

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: Let 𝕋 ⊂ 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∈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.

Date: 2012
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https://doi.org/10.1155/2012/707319

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:707319

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