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

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  • Erbil Çetin
  • F. Serap Topal

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.

Suggested Citation

  • Erbil Çetin & F. Serap Topal, 2012. "Periodic Solutions in Shifts 𠜹 ± for a Nonlinear Dynamic Equation on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, August.
    • Handle: RePEc:hin:jnlaaa:707319
    DOI: 10.1155/2012/707319
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