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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 41 Issue: 1

SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Murat Adıvar
Muhammad N. Islam
Youssef N. Raffoul
Sayfa
—
Yayın Tarihi
2012-01-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation.
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Temel Bulgular & Veri:Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction.
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Sonuç & Katkı:Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Krasnoselskii’s fixed point theorem · Large contraction · Periodic solution

Abstract

In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation. Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction. Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.

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Bu Makaleye Atıf Yap

Adıvar, M., Islam, M. N., Raffoul, Y. N. (2012). SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS. Hacettepe Journal of Mathematics and Statistics, Volume: 41 Issue: 1. https://ajindex.com/articles/1403570

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Kaynakça (8)

  1. Burton, T. A. Stability by Fixed Point Theory for Functional Differential Equations (Dover, New York, 2006).
  2. Kaufmann, E. R. and Raffoul, Y. N. Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale, Electron. J. Differential Equations No. 27, 12pp, 2007.
  3. Kaufmann, E. R. and Raffoul, Y. N. Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl. 319 (1), 315–325, 2006.
  4. Liu, Y. and Li, Z. Schaefer type theorem and periodic solutions of evolution equations, J. Math. Anal. Appl. 316, 237–255, 2006.
  5. Liu, Y. and Li, Z. Krasnoselskii type fixed point theorems and applications, Proc. Amer. Math. Soc. 136 (4), 1213–1220, 2008.
  6. Raffoul, Y. N. Periodic solutions for neutral nonlinear differential equations with functional delay, Electron. J. Differential Equations 102, 1–7, 2003.
  7. Raffoul, Y. N. Positive periodic solutions in neutral nonlinear differential equations, E. J. Qualitative Theory of Diff. Equ. 16, 1–10, 2007.
  8. Smart, D. R. Fixed Points Theorems (Cambridge Univ. Press, Cambridge, 1980).