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

Erbil Çetin and F. Serap Topal

Abstract and Applied Analysis, 2012, vol. 2012, 1-17

Abstract:

Let ð •‹ ⊂ â„ be a periodic time scale in shifts ð ›¿ ± . We use a fixed point theorem due to Krasnosel'skiĭ to show that nonlinear delay in dynamic equations of the form ð ‘¥ Δ ( ð ‘¡ ) = − ð ‘Ž ( ð ‘¡ ) ð ‘¥ 𠜎 ( ð ‘¡ ) + ð ‘ ( ð ‘¡ ) ð ‘¥ Δ ( ð ›¿ − ( 𠑘 , ð ‘¡ ) ) ð ›¿ Δ − ( 𠑘 , ð ‘¡ ) + ð ‘ž ( ð ‘¡ , ð ‘¥ ( ð ‘¡ ) , ð ‘¥ ( ð ›¿ − ( 𠑘 , ð ‘¡ ) ) ) , ð ‘¡ ∈ ð •‹ , has a periodic solution in shifts ð ›¿ ± . We extend and unify periodic differential, difference, â„Ž -difference, and ð ‘ž -difference equations and more by a new periodicity concept on time scales.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:707319

DOI: 10.1155/2012/707319

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